Decompression of surface normals in three-dimensional graphics data

ABSTRACT

Three-dimensional compressed geometry is decompressed with a unit having an input FIFO receiving compressed data bits and outputting to an input block state machine and an input block, whose outputs are coupled to a barrel shifter unit. Input block output also is input to Huffman tables that output to the state machine. The state machine output also is coupled to a data path controller whose output is coupled to a tag decoder, and to a normal processor receiving output from the barrel shifter unit The decompressor unit also includes a position/color processor that receives output from the barrel shifter unit. Outputs from the normal processor and position/color processor are multiplexed to a format converter. For instructions in the data stream that generate output to the format converter, the decompression unit generates a tag sent to the tag decoder in parallel with bits for normals that are sent to the format converter. The decompressed stream of triangle data may then be passed to a traditional rendering pipeline, where it can be processed in full floating point accuracy, and thereafter displayed or otherwise used.

CONTINUATION DATA

This application is a continuation of U.S. application Ser. No.09/028,387 (“Decompression of Surface Normals in Three-DimensionalGraphics Data” by Michael F. Deering) which was filed on Feb. 24, 1998now U.S. Pat. No. 6,088,034, which is a divisional of U.S. applicationSer. No. 08/511,326 (“Method and Apparatus for Decompression ofCompressed Geometric Three-Dimensional Graphics Data” by Michael F.Deering and Aaron S. Wynn) which was filed on Aug. 4, 1995 now U.S. Pat.No. 5,842,004, and is hereby incorporated by reference as though fullyand completely set forth herein.

FIELD OF THE INVENTION

The present invention relates generally to decompressing graphics data,and more particularly to methods and apparatuses that decompresscompressed three-dimensional geometry data.

BACKGROUND OF THE INVENTION

Modem three-dimensional computer graphics use geometry extensively todescribe three-dimensional objects, using a variety of graphicalrepresentation techniques. Computer graphics find wide use inapplications ranging from computer assisted design (“CAD”) programs tovirtual reality video games. Complex smooth surfaces of objects can besuccinctly represented by high level abstractions such as trimmednon-uniform rational splines (“NURBs”), and often detailed surfacegeometry can be rendered using texture maps. But adding more realismrequires raw geometry, usually in the form of triangles. Position,color, and normal components of these triangles are typicallyrepresented as floating point numbers, and describing an isolatedtriangle can require upwards of 100 bytes of storage space.

Understandably, substantial space is necessary for three-dimensionalcomputer graphics objects to be stored, e.g., on a computer hard disk orcompact disk read-only memory (“CD-ROM”). Similarly, considerable timein necessary for such objects to be transmitted, e.g., over a network,or from disk to main memory.

Geometry compression is a general space-time trade-off, and offersadvantages at every level of a memory/interconnect hierarchy. A similarsystems problem exists for storage and transmission of two-dimensionalpixel images. A variety of lossy and lossless compression anddecompression techniques have been developed for two-dimensional pixelimages, with resultant decrease in storage space and transmission time.Unfortunately, the prior art does not include compression/decompressiontechniques appropriate for three-dimensional geometry, beyond polygonreduction techniques. However, the Ph.D. thesis entitled Compressing theX Graphics Protocol by John Danskin, Princeton University, 1994describes compression for two-dimensional geometry.

Suitable compression can greatly increase the amount of geometry thatcan be cached, or stored, in the fast main memory of a computer system.In distributed networked applications, compression can help make sharedvirtual reality (“VR”) display environments feasible, by greatlyreducing transmission time.

Most major machine computer aided design (“MCAD”) software packages, andmany animation modeling packages use constructive solid geometry (“CSG”)and free-form NURBS to construct and represent geometry. Using suchtechniques, regions of smooth surfaces are represented to a high levelwith resulting trimmed polynomial surfaces. For hardware rendering,these surfaces typically are pre-tessellated in triangles using softwarebefore transmission to rendering hardware. Such softwarepre-tessellation is done even on hardware that supports some form ofhardware NURBS rendering.

However, many advantages associated with NURBS geometric representationare for tasks other than real-time rendering. These non-rendering tasksinclude representation for machining, interchange, and physical analysissuch as simulation of turbulence flow. Accurately representing trimmingcurves for NURBS is very data intensive, and as a compression technique,trimmed NURBS can not be much more compact than pre-tessellatedtriangles, at least at typical rendering tessellation densities.Finally, not all objects are compactly represented by NURBS. Althoughmany mechanical objects such as automobile hoods and jet turbine bladeshave large, smooth areas where NURBS representations can beadvantageous, many objects do not have such areas and do not lendthemselves to such representation. Thus, while NURBS will have manyapplications in modelling objects, compressed triangles will be far morecompact for many classes of application objects.

Photo-realistic batch rendering has long made extensive use of texturemap techniques to compactly represent fine geometric detail. Suchtechniques can include color texture maps, normal bump maps, anddisplacement maps. Texture mapping works quite well for large objects inthe far background, e.g., clouds in the sky, buildings in the distance.At closer distances, textures work best for three-dimensional objectsthat are mostly flat, e.g., billboards, paintings, carpets, marblewalls, and the like. More recently, rendering hardware has begun tosupport texture mapping, and real-time rendering engines can also applythese techniques.

However, texture mapping results in a noticeable loss of quality fornearby objects that are not flat. One partial solution is the“signboard”, in which a textured polygon always swivels to face theobserver. But when viewed in stereo, especially head-tracked VR stereo,nearby textures are plainly perceived as flat. In these instances, evena lower detail but fully three-dimensional polygonal representation of anearby object would be much more realistic.

Polyhedral representation of geometry has long been supported in thefield of three-dimensional raster computer graphics. In suchrepresentation, arbitrary geometry is expressed and specified typicallyby a list of vertices, edges, and faces. As noted by J. Foley, et al. inComputer Graphics: Principles and Practice, 2nd ed., Addison-Wesley,1990, such representations as winged-edge data structures were designedas much to support editing of the geometry as display. Vestiges of theserepresentations survive today as interchange formats, e.g., WavefrontOBJ. While theoretically compact, some compaction is sacrificed forreadability by using ASCII data representation in interchange files.Unfortunately, few if any of these formats can be directly passed asdrawing instructions to rendering hardware.

Another historical vestige in such formats is the support of N-sidedpolygons, a general primitive form that early rendering hardware couldaccept. However, present day faster rendering hardware mandates that allpolygon geometry be reduced to triangles before being submitted tohardware. Polygons with more than three sides cannot in general beguaranteed to be either planar or convex. If quadrilaterals are acceptedas rendering primitives, it is to be accepted that they will bearbitrarily split into a pair of triangles before rendering.

Modem graphics languages typically specify binary formats for therepresentation of collections of three-dimensional triangles, usually asarrays of vertex data structures. Thus, PHIGS PLUS, PEX, XGL, andproposed extensions to OpenGL are of this format form, and will definethe storage space taken by executable geometry.

It is known in the art to isolate or chain triangles in “zigzag” or“star” strips. For example, Iris-GL, XGL, and PEX 5.2 define a form ofgeneralized triangle strip that can switch from a zigzag to star-likevertex chaining on a vertex-by-vertex basis, but at the expense of anextra header word per vertex in XGL and PEX. A restart code allowsmultiple disconnected strips of triangles to be specified within onearray of vertices.

In these languages, all vertex components (positions, colors, normals)may be specified by 32-bit single precision IEEE floating point numbers,or 64-bit double precision numbers. The XGL, IrisGL, and OpenGL formatsalso provide some 32-bit integer support. The IrisGL and OpenGL formatssupport vertex position component inputs as 16-bit integers, and normalsand colors can be any of these as well as 8-bit components. In practice,positions, colors, and normals can be quantized to significantly fewerthan 32 bits (single precision IEEE floating point) with little loss invisual quality. Such bit-shaving may be utilized in commercialthree-dimensional graphics hardware, providing there is appropriatenumerical analysis support.

However compressed, geometric data including three-dimensional geometrydata must be decompressed to be useful. For example, applicant's patentapplication Ser. No. 08/511,294 filed Aug. 4, 1995, entitled METHOD ANDAPPARATUS FOR GEOMETRIC COMPRESSION OF THREE-DIMENSIONAL GRAPHICS DATA,assigned to the assignee herein, discloses such compression.

Thus, there is a need for method and apparatus for decompressingthree-dimensional geometry that has been compressed. Preferably,decompression is such that the output data may be passed to renderinghardware directly as drawing instructions. Finally, decompression ofthree-dimensional geometry should be implementable using hardware,software, or a combination thereof.

The present invention discloses such decompression.

SUMMARY OF THE PRESENT INVENTION

For decompression according to the present invention, three-dimensionalgeometry is first represented as a generalized triangle mesh, whichallows each instance of a vertex in a linear stream to specify anaverage of between ⅓ triangle and 2 triangles. Individual positions,colors, and normals are quantized, with a variable length compressionbeing applied to individual positions, colors, and normals. Quantizedvalues are delta-compression encoded between neighbors to provide vertextraversal orders, and mesh buffer references are created. Histograms ofdelta-positions, delta-normals and delta-colors are created, after whichvariable length Huffman tag codes, as well as delta-positions,delta-normals and delta-colors are created. The compressed output binarystream includes the output Huffman table initializations, ordered vertextraversals, output tags, and the delta-positions, delta-normals, anddelta-colors.

Decompression of such compressed three-dimensional geometry data may beimplemented in hardware, software, or a combination of each. Thedecompression unit includes an input FIFO that receives compressed databits and a signal noting size of the incoming data. The FIFO outputs arecoupled to an input block state machine and an input block. Outputs fromthe input block and input block state machine are coupled to a barrelshifter unit. Input block output also is input to Huffman tables thatoutput to the state machine. The state machine output also is coupled toa data path controller whose output is coupled to a tag decoder, and toa normal processor receiving output from the barrel shifter unit. Thedecompressor unit also includes a position/color processor that receivesoutput from the barrel shifter unit. Outputs from the normal processorand position/color processor are multiplexed to a format converter.

For instructions in the data stream that generate output to the formatconverter, the decompression unit generates a 12-bit tag that is sent tothe tag decoder in parallel with bits for normals that are sent to theformat converter. A read-back path is used to read back the internalstate of the decompressor unit. The decompressor unit carries out thefollowing procedures:

(1) Fetch the rest of the next instruction, and the first 8 bits of thefollowing instruction;

(2) Using the tag table, expand any compressed value fields to fullprecision;

(3A) If values are relative, add to current value; otherwise replace;

(3B) If mesh buffer reference, access old values;

(3C) If other command, do housekeeping;

(4) If normal, pass index through ROM table to obtain full values;

(5) Output values in generalized triangle strip form to next stage.

The decompressed stream of triangle data may then be passed to atraditional rendering pipeline, where it can be processed in fullfloating point accuracy, and thereafter displayed or otherwise used.

Other features and advantages of the invention will appear from thefollowing description in which the preferred embodiments have been setforth in detail, in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a generalized network system over which compressedthree-dimensional geometry may be transmitted for decompression,according to the present invention, at the receiving end;

FIG. 2 depicts a generalized triangular mesh data structure, andgeneralized mesh buffer representation of surface geometry;

FIG. 3 depicts six-way sign-bit and eight-way octant symmetry in a unitsphere, used to provide forty-eight way reduction in table look-up size;

FIG. 4A depicts a vertex command in a geometry compression instructionset;

FIG. 4B depicts a normal command in a geometry compression instructionset;

FIG. 4C depicts a color command in a geometry compression instructionset;

FIG. 4D depicts a mesh buffer reference command in a geometrycompression instruction set;

FIG. 4E depicts a set state instruction in a geometry compressioninstruction set;

FIG. 4F depicts a set table command instruction in a geometrycompression instruction set;

FIG. 4G depicts a pass through command instruction in a geometrycompression instruction set;

FIG. 4H depicts a variable length no-op command instruction in ageometry compression instruction set;

FIG. 4I depicts tag and Δ-position data structure;

FIGS. 4J-1 and 4J-2 depict alternative tag and Δ-normal data structure;

FIG. 4K depicts tag and Δ-color data structure;

FIG. 5 is a flowchart of method steps in a geometry compressionalgorithim;

FIG. 6 is a simplified block diagram of decompressor hardware, accordingto the present invention;

FIG. 7 is a detailed overall block diagram of a decompressor unit,according to the present invention;

FIG. 8 is a detailed block diagram of the input block shown in FIG. 7;

FIG. 9 is a detailed block diagram of the barrel shifter unit shown inFIG. 7;

FIG. 10 is a detailed block diagram of the position/color processor unitshown in FIG. 7;

FIG. 11A is a detailed block diagram of the normal processor unit shownin FIG. 7;

FIG. 11B is a detailed block diagram showing the decoder, fold, and ROMlook-up components associated with the normal processor unit of FIG.11A;

FIG. 12 is a block diagram showing interfaces to a mesh buffer, as shownin FIG. 10 and/or FIG. 11A;

FIG. 13A depicts interfaces to Huffman tables, according to the presentinvention;

FIG. 13B depicts a preferred format for entry of the Huffman table data,according to the present invention;

FIG. 14A depicts a vertex instruction, according to the presentinvention;

FIG. 14B depicts vertex component data formats, according to the presentinvention;

FIG. 14C depicts the format for the set normal instruction, according tothe present invention;

FIG. 14D depicts a set color instruction, according to the presentinvention;

FIG. 14E depicts a mesh buffer reference instruction, according to thepresent invention;

FIG. 14F depicts a set state instruction, according to the presentinvention;

FIG. 14G depicts a set table instruction, according to the presentinvention;

FIG. 14H depicts a passthrough instruction, according to the presentinvention;

FIG. 14I depicts a variable-length NOP instruction, according to thepresent invention; and

FIG. 14J depicts a skip 8 instruction, according to the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

A graphics decompressor according to the present invention decompressesthree-dimensional graphics objects. Three-dimensional compression ofsuch geometry advantageously permits a reduction in the time needed totransmit the compressed three-dimensional geometry, e.g., over anetwork, as well a reduction of the space wherein the geometry may bestored, e.g., on a CD-ROM, or the like.

Before describing decompression of compressed three-dimensionalgraphics, the overall environment in which the present invention may bepracticed will be described with respect to FIG. 1.

FIG. 1 depicts a generalized network over which three-dimensionalcompressed geometry data may be transmitted, and decompressed usingsoftware, hardware, or a combination of each at the receiving end. Ofcourse, decompression of three-dimensional graphics compressionaccording to the present invention may be practiced upon compressed datathat is presented other than via a network, e.g., compressed data storedin a memory, on a CD-ROM, and the like.

As shown in FIG. 1, a source of three-dimensional graphics data 10 maybe coupled to a server or encoder system 20 whose processed andcompressed output is coupled over one or more networks 30 to one or moretarget clients or decoder systems 40. The network may be homogeneous,heterogeneous, or point-to-point.

Server 20 includes a central processing unit 50 that includes a centralprocessor unit per se (“CPU”) 60 with associated main memory 70, a meshbuffer 80, a memory portion 90 that may include a compression algorithm,and a region of read-only-memory (“ROM”) 100. Alternatively, compressionaccording may be carried out in hardware as opposed to software.ATTACHMENT 1 is a copy of a code listing for such a compressionalgorithm as described in the above-referenced patent application.Server 20 also includes a three-dimensional graphics compression unit60, whose compressed output data is arranged by a disk layout unit 70for storage onto storage disk unit 80, which may include one or moreCD-ROMs. The server communicates over the network(s) 30 via networkinterface unit 10. Those skilled in the art will appreciate that server20 may include a mechanism for arbitrating between a plurality ofclient-decoder requests for compressed data.

As described in applicant's patent application Ser. No. 08/511,294 filedAug. 4, 1995, entitled METHOD AND APPARATUS FOR GEOMETRIC COMPRESSION OFTHREE-DIMENSIONAL GRAPHICS DATA, assigned to the assignee herein, lossycompression of three-dimensional geometric data can produce ratios of6:1 to 10:1, with little loss in displayed object quality. The followingportions of this Specification will describe compression, as set forthin the above-referenced patent application, to facilitate a betterunderstand of decompression, according to the present invention.

In a network environment, at the receiving end, decoder systems(s) 40include a network interface unit 120, a unit 130, according to thepresent invention, that decompresses three-dimensional graphics data,and whose output is coupled to a three-dimensional graphics renderingunit 140. System 40 further comprises a central processing system 150that includes a CPU 160, memory 170, a portion of which 180 may includedecompression software, and ROM 190. Compressed three-dimensionalgraphics may advantageously be decompressed using software, hardware, ora combination of each. The decompressed output from decoder 40 furthermay be coupled to a viewer 200, or to another system requiring thedecompressed graphics. Of course, unit 40 may be a standalone unit, intowhich precompressed three-dimensional graphics are coupled from storage82, disks or CD-ROM 84, or the like, for decompression. Unit 40 may, forexample, comprise a computer or workstation.

Assuming that three-dimensional graphics compression unit 60 functionsas described in applicant's above-noted patent application, triangledata will have first been converted into a generalized triangle mesh.For a given fixed capacity of storage medium 80, a triangle mesh datastructure is a near-optimal representation of triangle data. In thepreferred embodiment, three-dimensional graphics object may berepresented as three-dimensional triangular data, whose format afterconversion causes each linear strip vertex, on average, to specify fromabout ⅓ triangles to about 2 triangles. Further, such triangle stripstructure permits extraction of the compressed geometry by a singlemonotonic scan over the vertex array data structure.

FIG. 2 depicts a generalized triangular mesh data structure, andgeneralized mesh buffer representation of surface geometry. Such a meshdata structure may be used in three-dimensional geometry compression,although by confining itself to linear strips, a generalized trianglestrip format wastes a potential factor of two in space. The geometryshown in FIG. 2, for example, can be represented by one triangle strip,but many interior vertices will appear twice in the strip.

In FIG. 2, a generalized triangle strip may be defined as follows, wherethe R denotes restart, O denotes replace oldest, M denotes replacemiddle, and a trailing letter p denotes push into mesh buffer. Thenumber following a capital letter is a vertex number, and a negativenumber is the mesh buffer reference, in which −1 denotes the most recentpushed vertex.

R6, O1, O7, O2, O3, M4, M8, O5, O9, O10, M11

M17, M16, M9, O15, O8, O7, M14, O13, M6,

O12, M18, M19, M20, M14, O21, O15, O22, O16,

O23, O17, O24, M30, M29, M28, M22, O21, M20,

 M27, O26, M19, O25, O18

Using the same nomenclature, a generalized triangle mesh may be definedas follows:

R6p, O1, O7p, O2, O3, M4, M8p, O5, O9p, O10, M11,

M17p, M16p, M-3, O15p, O-5, O6, M14p, O13p, M9,

O12, M18p, M19p, M20p, M-5, O21p, O-7, O22p, O-9,

O23, O-10, O-7, M30, M29, M28, M-1, O-2, M-3,M27,

O26, M4, O-25, O-5

It is to be noted that a vertex reference advantageously can beconsiderably more compact (e.g., be represented by fewer bits) than afull vertex specification.

Three-dimensional geometry compression explicitly pushes old vertices(e.g., vertices with a trailing letter “p” above) into a queueassociated with mesh buffer memory 80 (see FIG. 1). These old verticeswill later be explicitly referenced when the old vertex is desiredagain. This approach provides a fine control that supports irregularmeshes of nearly any shape. Buffer memory 80 has finite length, and inpractice a maximum fixed queue length of 16 is used, which requires a4-bit index. With respect to the compression of three-dimensionalgraphics, the term “mesh buffer” shall refer to this queue, and theexpression “generalized triangle mesh” will refer to a combination ofgeneralized triangle strips and mesh buffer references.

The fixed size of mesh buffer 80 requires all tessellators/re-strippersfor compressed geometry to break-up any runs longer than sixteen uniquereferences. However, as geometry compression typically will not beprogrammed directly at the user level but rather by sophisticatedtessellators/reformatters, a non-onerous restriction. Sixteen oldvertices can in fact permit avoiding re-specification of up to about 94%of the redundant geometry.

FIG. 2 also is an example of a general mesh buffer representation ofsurface geometry. Geometry compression language supports the four vertexreplacement codes of generalized triangle strips, namely: replaceoldest, replace middle, restart clockwise, and restart counterclockwise.Further, the language adds an additional bit in each vertex header toindicate whether or not this vertex should be pushed into the meshbuffer. In one embodiment, the mesh buffer reference command has a 4-bitfield to indicate which old vertex should be re-referenced, along withthe 2-bit vertex replacement code. Mesh buffer reference commands do notcontain a mesh buffer push bit; old vertices can only be recycled once.

In practice, geometry rarely is comprised purely of positional data andin general, a normal, and/or color, and/or texture map coordinate arealso specified per vertex. Accordingly, entries into mesh buffer 80contain storage for all associated per-vertex information, specificallyincluding normal and color and/or texture map coordinate.

For maximum storage space efficiency, when a vertex is specified in thedata stream, per vertex normal and/or color information preferably isdirectly bundled with the position information. Preferably, suchbundling is controlled by two state bits: bundle normals with vertices(BNV), and bundle colors with vertices (BCV). FIG. 4E depicts a commandstructure including bits, among others. When a vertex is pushed into themesh buffer, these bits control if its bundled normal and/or color arepushed as well.

It should be noted that the compression technique described in theabove-referenced patent application is not limited to triangles, andthat vectors and dots may also be compressed. Lines, for example, are asubset of triangles, in which replacement bits are MOVE and DRAW. Anoutput vertex is then a vertex that represents one end point of a linewhose other vertex is the most recently, previously omitted vertex. Fordots, the replacement bits are DRAW, and an output vertex is the vertex.

When CPU 52 executes a mesh buffer reference command, this process isreversed. That is, the two bits specify whether a normal and/or colorshould be inherited, or read, from the mesh buffer storage 80, orobtained from the current normal or current color. Software 58preferably includes explicit commands for setting these two currentvalues. An exception to this rule exists, however, when an explicit “setcurrent normal” command is followed by a mesh buffer reference, with theBNV state bit active. In this situation, the former overrides the meshbuffer normal, to allow compact representation of hard edges in surfacegeometry. Analogous semantics are also defined for colors, allowingcompact representation of hard edges in surface colors.

Two additional state bits control the interpretation of normals andcolors when the stream of vertices is converted into triangles. Areplicate normals over triangle (RNT) bit indicates that the normal inthe final vertex that completes a triangle should be replicated over theentire triangle. A replicate colors over triangle (RCT) bit is definedanalogously, as shown in the command structure of FIG. 4E.

Compression of image xyz positions will now be described. Use of the8-bit exponent associated with 32-bit IEEE floating-point numbers allowspositions to range in size from sub-atomic particles to billions oflight years. But for any given tessellated object, the exponent isactually specified just once by a current modeling matrix, and objectgeometry is effectively described within a given modeling space usingonly a 24-bit fixed-point mantissa. In many cases far fewer bits areneeded for visual acceptance, and the geometry compression languagepreferably supports variable quantization of position data down to onebit.

At the other extreme, empirical visual tests as well as well asconsideration of semiconductor hardware implementation indicate that nomore than 16 bits of precision per component of position is necessaryfor nearly all cases.

Assume, however, that the position and scale of local modeling space perobject are specified by full 32-bit or 64-bit floating-pointcoordinates. Using sufficient numerical care, multiple such modelingspaces may be combined together to form seamless geometry coordinatesystems with much greater than 16-bit positional precision.

Most geometry is local. Thus, within a 16-bit (or less) modeling spacefor each object, the difference (Δ) between adjacent vertices in thegeneralized mesh buffer stream is likely to be less than 16 bits insignificance. If desired, one may construct a histogram representing bitlength of neighboring position Δ's in a batch of geometry, and basedupon this histogram assign a variable length code to compactly representthe vertices. As will be described, preferably customized Huffman codingis used to encode for the positional Δ's in the geometry compression.

Compression of red-blue-green-alpha (“RBGA”) colors will now bedescribed. Color data are treated similarly to positions, but with asmaller maximum accuracy. Thus, RGBΔ color data are first quantized to12-bit unsigned fraction components that are absolute linearreflectivity values (in which 1.0 represents 100% reflectivity). Anadditional parameter allows color data effectively to be quantized toany amount less than 12 bits. By way of example, colors may all bewithin a 5-5-5 RGB color space, as shown in FIG. 4C. The optional Δfield is controlled by a color Δ present (“CAP”) state bit shown in FIG.4E. On the final rendered image individual pixel colors are stillinterpolated between the quantized vertex colors, and also typically aresubject to lighting.

In practice, the same Δ-coding may be used for color components and forpositions. The area of color data compression is where geometrycompression and traditional image compression confront the most similarproblems. However, many advanced image compression techniques may beavoided for geometry color compression because of the difference infocus.

For example, the JPEG image compression standard relies upon assumptionsabout viewing of the decompressed data that cannot be made for geometrycompression. For example, in image compression, it is known a priorithat the pixels appear in a perfectly rectangular array, and that whenviewed, each pixel subtends a narrow range of visual angles. Bycontrast, in geometry compression, the relationship between the viewerand the rasterized geometry is unpredictable.

In image compression, it is known that the spatial frequency of thedisplayed pixels upon on the viewer's eyes is likely higher than thecolor acuity of the human visual system. For this reason, colors arecommonly converted to YUV space so that the UV color components can berepresented at a lower spatial frequency than the Y (intensity)component. Usually digital bits representing sub-sampled UV componentsare divided among two or more pixels. However, geometry compressioncannot take advantage of this because there is no fixed display scale ofthe geometry relative to the viewer's eye. Further, given thatcompressed triangle vertices are connected to four to eight or moreother vertices in the generalized triangle mesh, there is no consistentway of sharing “half” the color information across vertices.

Similar arguments apply for the more sophisticated transforms used intraditional image compression, such as the discrete cosine transform.These transforms assume a regular (rectangular) sampling of pixelvalues, and require a large amount of random access duringdecompression.

It is known in the art to use pseudo-color look-up tables, but suchtables would required a fixed maximum size, and would represent arelatively expensive resource for real-time processing. Whilepseudo-color indices could yield slightly higher compression ratios forcertain scenes, the RGB model is more generalized and considerably lessexpensive to implement.

In an RGB model, RGB values are represented as linear reflectancevalues. Theoretically, if all effects of lighting could be known apriori, one or two representation bits could be dropped if the RGBcomponents had been represented in a nonlinear, or perceptually linearspace (sometime referred to as gamma corrected space). In practice,lighting effects tend not to be predictable, and on-the-fly conversionfrom nonlinear light to linear light would require considerable hardwareresources.

The compression of surface normals will now be described. Traditionally96-bit normals (three 32-bit IEEE floating-point numbers) are used incalculations to determine 8-bit color intensities. Theoretically, 96bits of information could be used to represent 2⁹⁶ different normals,spread evenly over the surface of a unit sphere. The resultant extremelyhigh accuracy represents a normal projecting in any direction every 2⁻¹⁶radians.

But for IEEE floating-point normalized normals, the exponent bits areeffectively unused. Given the constraint M_(x) ²+N_(y) ²+N_(z) ²=1, atleast one of N_(x), N_(y), or N_(z) must be in the 0.5 to 1.0 range.During rendering, this normal will be transformed by a compositemodeling orientation matrix:

N′ _(x) =N _(x) ·T _(0,0) +N _(y) ·T _(O,1) +N _(z) ·T _(O,2)

N′ _(y) =N _(x) ·T _(1,O) +N _(y) ·T _(1,1) +N _(z) ·T _(1,2)

N′ _(z) =N _(x) ·T _(2,O) +N _(y) ·T _(2,1) +N _(z) ·T _(2,2)

Assuming a typical implementation in which lighting is performed inworld coordinates, the view transform is not involved in the processingof normals. If the normals have been pre-normalized, then to avoidredundant re-normalization of the normals, the composite modelingtransformation matrix T is typically pre-normalized to divide out anyscale changes. Thus:

T _(0,0) ² +T _(1,0) ² +T _(2,0) ²=1, etc.

During normal transformation, floating-point arithmetic hardwareeffectively truncates all additive arguments to the accuracy of thelargest component. The result is that for a normalized normal undergoingtransformation by a scale preserving modeling orientation matrix, thenumerical accuracy of the transformed normal value is reduced to no morethan 24-bit fixed-point accuracy in all but a few special cases.

By comparison, even 24-bit normal components would still provide higherangular accuracy than the repaired Hubble space telescope, and inpractice, some systems utilize only 16-bit normal components. Inempirical tests with 16-bit normal components, results from an angulardensity of 0.01 radians between normals (e.g., about 100,000 normalsdistributed over a unit sphere) are not visually distinguishable fromfiner representations. In rectilinear space, these normals still requirehigh representation accuracy and in practice, 16-bit componentsincluding one sign and one guard bit represents a good design choice.This still requires 48 bits to represent a normal, but since only100,000 specific normals are of interest, theoretically a single 17-bitindex could denote any of these normals.

The use of normals as indices, and the resultant advantages providedwill now be described. One method of converting an index of a normal onthe unit sphere back into a N_(x), N_(y), N_(z) value is with a tablelook-up, the table being loaded into memory 70 perhaps. Although tablesize is potentially large, the requisite size can be substantiallyreduced by taking advantage of a 48-way symmetry present in the unitsphere.

More particularly, as shown by FIG. 3, the unit sphere is symmetrical bysign bits in the eight quadrants by sign bits. By allowing three of thenormal representation bits to be the three sign bits of the xyzcomponents of a normal, it then is only necessary to represent oneeighth of the unit sphere. Each octant of the unit sphere can be dividedinto six identical components by folding about the planes x=y, x=z, andy=z. The six possible sextants are encoded with another three bits,which leaves only {fraction (1/48)} of the sphere remains to berepresented.

Utilizing the above-noted symmetry reduces the look-up table size by afactor of 8×6=48. Instead of storing 100,000 entries, the look-up tableneed store only about 2,000 entries, a size small enough to be anon-chip ROM look-up table, stored perhaps within ROM 59 (see FIG. 1).Indexing into the look-up table requires 11 address bits, which whenadded to the previously described two 3-bit fields results in a 17-bitfield to describe all three normal components.

Representing a finite set of unit normals is equivalent to positioningpoints on the surface of the unit sphere. Although no perfectly equalangular density distribution exists for large numbers of points, manynear-optimal distributions exist. Theoretically, a distribution havingthe above-described type of 48-way symmetry could be used for thedecompression look-up table associated with the three-dimensionalgeometry decompression unit 130 (see FIG. 1).

However, several additional constraints mandate a different choice ofencoding. First, a scalable density distribution is desired, e.g., adistribution in which setting in the look-up table more low orderaddress bits to “0” still results in fairly even normal density on theunit sphere. Otherwise a different look-up table for every encodingdensity would be required. Secondly, a Δ-encodable distribution isdesired in that adjacent vertices in geometry statistically have normalsthat are nearby on the surface of the unit sphere. Nearby locations onthe two-dimensional space of the unit-sphere surface are most succinctlyencoded by a two-dimensional offset. It is desirable to have adistribution in which such a metric exists. Finally, althoughcomputational costs associated with the normal encoding process are notcritically important, distributions having lower encoding costs arestill preferred.

Compression according to the above-referenced patent applicationutilizes a distribution having a regular grid in the angular spacewithin one sextant of the unit sphere. As such, rather than a monolithic11-bit index, all normals within a sextant are advantageouslyrepresented with two 6-bit orthogonal angular addresses. Thisconfiguration then revises the previous bit-total to 18-bits. As was thecase for positions and colors, if more quantization of normals isacceptable, these 6-bit indices can be reduced to fewer bits, and thusabsolute normals can be represented using anywhere from 18 to as few as6 bits. However, as described below, this space preferably is Δ-encodedto further reducing the number of bits required for high qualityrepresentation of normals.

Normal encoding parameterization will now be described. Points on a unitradius sphere are parameterized using spherical coordinates by angles θand φ, where θ is the angle about the y axis and φ is the longitudinalangle from the y=0 plane. Equation (1) governs mapping betweenrectangular and spherical coordinates as follows:

x=cos θ cos φ y=sin φ z=sin θ cos φ  (1)

Points on the sphere are folded first by octant, and then by sort orderof xyz into one of six sextants. All table encoding takes place in thepositive octant in the region bounded by the half spaces:

x≧z z≧y y≧0

As shown in FIG. 3, the described triangular-shaped patch runs from 0 toπ/4 radians in θ, and from 0 to a maximum 0.615479709 radians in φ.

Quantized angles are represented by two n-bit integers {circumflex over(θ)}_(n) and {circumflex over (θ)}_(n), where n is in the range of 0 to6. For a given n, the relationship between indices θ and φ is:$\begin{matrix}\begin{matrix}{{\Theta \left( {\hat{\Theta}}_{n} \right)} = {\arcsin \quad \tan \frac{\left( {\varphi_{\max}{\bullet \left( {n - {\hat{\Theta}}_{n}} \right)}} \right.}{2^{n}}}} \\{{\varphi \left( {\hat{\varphi}}_{n} \right)} = \frac{\varphi_{\max}{\bullet\varphi}}{2^{n}}}\end{matrix} & (2)\end{matrix}$

Equations (2) show how values of {circumflex over (θ)}_(n) and{circumflex over (φ)}_(n) can be converted to spherical coordinates θand φ, which in turn can be converted to rectilinear normal coordinatecomponents via equation (1).

To reverse the process, e.g. to encode a given normal N into {circumflexover (θ)}_(n) and {circumflex over (φ)}_(n), one cannot simply invertequation (2). Instead, the N must be first folded into the canonicaloctant and sextant, resulting in N′. Then N′ must be dotted with allquantized normals in the sextant. For a fixed n, the values of{circumflex over (θ)}_(n) and {circumflex over (φ)}_(n) that result inthe largest (nearest unity) dot product define the proper encoding of N.Other, more efficient methods for finding the correct values of{circumflex over (θ)}_(n) and {circumflex over (φ)}_(n) exist, forexample indexing through the table to set φ, and then jumping into θ.

At this juncture, the complete bit format of absolute normals can begiven. The uppermost three bits specify the octant, the next three bitsthe sextant, and finally two n-bit fields specify {circumflex over(θ)}_(n) and {circumflex over (φ)}_(n). The 3-bit sextant field takes onone of six values, the binary codes for which are shown in FIG. 3.

Some further details are in order. The three normals at the corners ofthe canonical patch are multiply represented, namely 6, 8, and 12 times.By employing the two unused values of the sextant field, these normalscan be uniquely encoded as 26 special normals.

This representation of normals is amenable to Δ-encoding, at leastwithin a sextant, although with some additional work, this can beextended to sextants that share a common edge. The Δ code between twonormals is simply the difference in {circumflex over (θ)}_(n) and{circumflex over (φ)}_(n), namely Δ{circumflex over (θ)}_(n) andΔ{circumflex over (φ)}_(n).

In the above-described patent application, compression tags are used,with a variation of a conventional Huffman algorithm. The Huffmancompression algorithm takes in a set of symbols to be represented, alongwith frequency of occurrence statistics (e.g., histograms) of thosesymbols. From this, variable length, uniquely identifiable bit patternsare generated that allow these symbols to be represented with anear-minimum total number of bits, assuming that symbols do occur at thefrequencies specified.

Many compression techniques, including JPEG, create unique symbols astags to indicate the length of a variable-length data-field thatfollows. This data field is typically a specific-length delta value.Thus, the final binary stream consists of (self-describing length)variable length tag symbols, each immediately followed by a data fieldwhose length is associated with that unique tag symbol.

In the referenced patent application, binary format for geometrycompression uses this technique to represent position, normal, and colordata fields. For geometry compression, these <tag, data> fields areimmediately preceded by a more conventional computer instruction setop-code field. These fields, along with potential additional operandbits, will be referred to as geometry instructions (see FIGS. 4A-4K).

Traditionally, each value to be compressed is assigned its ownassociated label, e.g. an xyz Δ position would be represented by threetag-value pairs. But since the Δxyz values are not uncorrelated, adenser, simpler representation can be attained. In general, the xyz Δ'sstatistically point equally in all directions in space. Thus, if n isthe number of bits needed to represent the largest of the Δ's, thenstatistically the other two Δ values require an average of n−1.4 bitsfor their representation. In practice, a single field-length tag may beused to indicate the bit length of Δx, Δy, and Δz.

Unfortunately, using this approach prevents taking advantage of anotherHuffman technique to save somewhat less than one more bit per component.However, the implemented embodiment outweighs this disadvantage by nothaving to specify two additional tag fields (for Δy and Δz). A furtheradvantage is that using a single tag field permits a hardwaredecompression engine to decompress all three fields in parallel, ifdesired.

Similar arguments hold for Δ's of RGBα values, and accordingly a singlefield-length tag is used to indicate bit-length of the R, G, B and, ifpresent, α, fields.

Absolute and Δ normals are also parameterized by a single value (n) thatcan be specified by a single tag. To facilitate high-speed, low-costhardware implementations, the length of the Huffman tag field may belimited to six bits, a relatively small value. A 64-entry tag look-uptable allows decoding of tags in one clock cycle. One table exists forpositions, another table exists for normals, and yet another tableexists for colors (and optionally, also for texture coordinates). Eachtable contains the length of the tag field, the length of the datafield(s), a data normalization coefficient, and an absolute/relativebit.

For reasonable hardware implementation, an additional complication mustbe addressed. As described below, all instruction are broken-up into aneight-bit header, and a variable length body, sufficient informationbeing present in the header to determine the body length. But the headerof one instruction must be placed in the data stream before the body ofthe previous instruction to give the hardware time to process the headerinformation. For example, the sequence . . . B0 H1B1 H2B2 H3 . . . hasto be encoded as . . . H1 B0 H2 B1 H3 B2 . . .

The geometry compression instruction set disclosed in theabove-referenced patent application will now be described with respectto FIGS. 4A-4K. FIG. 4A depicts a vertex command that specifies aHuffman compressed Δ-encoded position, as well as possibly a normaland/or color, depending on bundling bits (BNV and BCV). Two additionalbits specify a vertex replacement code (REP), and another bit controlsmesh buffer pushing of this vertex (MBP).

As shown in FIG. 4B, a normal command specifies a new current normal andthe color command shown in FIG. 4C depicts a new current color. Thenormal command and color command each use Huffman encoding of Δ values.

The mesh buffer reference command structure is shown in FIG. 4D. Themesh buffer reference command allows any of the sixteen most recentlypushed vertices (and associated normals and/or colors) to be referencedas the next vertex. As further shown in FIG. 4D, A 2-bit vertexreplacement (“REP”) code is also specified.

FIG. 4E depicts the set state instruction that updates the five statebits: RNT, RCT, BNV, BCV, and CAP.

FIG. 4F depicts a set table command, which is used to set entries to theentry value specified in one of the three Huffman decoding tables(Position, Normal, or Color).

FIG. 4G depicts a passthrough command that allows additional graphicsstate not controlled directly by geometry compression to be updatedin-line.

FIG. 4H depicts a variable length no-op (“VNOP”) command that allowsfields within the bit stream to be aligned to 32-bit word boundaries.This permits aligned fields to be efficiently patched at run-time by thegeneral CPU 52.

FIGS. 4I, 4J-1 and 4J-2 and 4K respectively depict tag and Δ-positiondata structure, tag and Δ-normal data structure, and tag and Δ-colordata structure. In FIGS. 4I and 4K, either absolute values of x, y, zare used, or delta values of x, y, and z are to be used.

Of course, other instruction sets may instead be used to compressthree-dimensional geometry.

The ratio of the time required for compression relative to decompressioncan be important. In practice, it is acceptable for off-line imagecompression to take up to perhaps sixty-times more time thandecompression, but for real-time video conferencing, the ratio should beone.

Advantageously, geometry compression does not have this real-timerequirement. Even if geometry is constructed on the fly, most geometrycreating techniques, e.g., CSG, require orders of magnitude more timethan needed for displaying geometry. Also, unlike continuous imagesfound in movies, in most applications of geometry compression acompressed three-dimensional object will be displayed for manysequential frames before being discarded. Should the three-dimensionalobject require animating, animation is typically done with modelingmatrices. Indeed for a CD-based game, it is quite likely that an objectwill be decompressed billions of times by customer-users, but will havebeen compressed only once by the authoring company.

Like some other compression systems, geometry compression algorithms canhave a compression-time vs. compression-ratio trade-off. For a givenquality target level, as allowable time for compression increases, thecompression ratio achieved by a geometry compression system increases.There exists a corresponding “knob” for quality of the resultingcompressed three-dimensional object, and lower the quality knob, thebetter the compression ratio achieved.

Aesthetic and subjective judgment may be applied to geometrycompression. Some three-dimensional objects will begin to appear badwhen target quantization of normals and/or positions is slightlyreduced, whereas other objects may be visually unchanged even with alarge amount of quantization. Compression can sometimes cause visibleartifacts, but in other cases may only make the object look different,not necessarily lower in quality. In one experiment by applicant, animage of an elephant actually begin to appear more realistic, with morewrinkle-like skin, as the image normals were quantized more. Once amodel has been created and compressed, it can be put into a library, tobe used as three-dimensional clip-art at the system level.

While many aspects of geometry compression are universal, theabove-described geometry compression instruction set has been somewhattailored to permit low-cost, high-speed hardware implementations. (It isunderstood that a geometry compression format designed purely forsoftware decompression would be somewhat different.). The describedgeometry compression instruction set is especially amenable to hardwareimplementation because of the one-pass sequential processing, limitedlocal storage requirements, tag look-up (as opposed to a conventionalHamming bit-sequential processing), and use of shifts, adds, andlook-ups to accomplish most arithmetic steps.

FIG. 5 is a flowchart outlining method steps in a geometry compressionalgorithm routine, described in the above-referenced patent application,with which the present decompression invention may be used. Such routinemay be stored in memory 80 and executed under control of CPU 60 (seeFIG. 1).

At step 200, an object is represented by an explicit group of trianglesto be compressed, along with quantization thresholds for positions,normals, and colors. At step 210, a topological analysis of connectivityis made, and hard edges are marked in normals and/or color, if suchinformation is not already present.

At step 220, vertex traversal order and mesh buffer references arecreated, and at step 230 histograms of Δ-positions, Δ-normals, andΔ-colors is created. At step 240, separate variable length Huffman tagcodes are assigned for the Δ-positions, Δ-normals, and Δ-colors, basedupon histographs.

At step 250, a binary output stream is generated by first outputtingHuffman table initialization, after which the vertices are traversed inorder. Appropriate tags and Δ's are output for all values.

Applicant has implemented a Wavefront OBJ format compressor thatsupports compression of positions and normals, and creates fullgeneralized triangle strips, but does not yet implement a fullmeshifying algorithm. Future embodiments will explore variable precisiongeometry, including fine structured updates of the compression tables.The current compressor expends time calculating geometric detailsalready known to the tessellator, and ultimately it is hoped to generatecompressed geometry directly. However, even its present unoptimizedstate, applicant's software can compress about 3,000 triangles/second inmany cases.

The present invention is directed to decompressing three-dimensionalcompressed geometry, at the user end of FIG. 1. ATTACHMENT 2 is alisting of an algorithm for decompression, according to the presentinvention. Briefly, in general, an applicable geometry decompressionalgorithm according to the present invention may be outlined as follows:

(1) Fetch the rest of the next instruction, and the first 8 bits of thefollowing instruction;

(2) Using the tag table, expand any compressed value fields to fullprecision;

(3A) If values are relative, add to current value; otherwise replace;

(3B) If mesh buffer reference, access old values;

(3C) If other command, do housekeeping.

(4) If normal, pass index through ROM table to obtain full values.

(5) Output values in generalized triangle strip form to next stage.

In the preferred embodiment, a software embodiment of applicant'sdecompressor decompresses compressed geometry at a rate of about 10,000triangles/second. A simplified overall block diagram of decompressionaccording to the present invention is shown in FIG. 6. A hardwareimplementation of a decompressor according to the present invention candecompress in the range of tens of millions of triangles/second, whichrate may be substantially expanded.

Before describing decompression, it is helpful to examine the results ofthe above-described compression techniques. Table 1, shown below,describes these results for several graphical objects: a triceratops, aSpanish galleon, a Dodge Viper, a '57 Chevy, and an insect. Generallyspeaking, Table 1 shows that positional quantization much above 24 bits(from an original 32 bits per x/y/z coordinate) has no significantvisible effects unless zooming is performed on the object. Positionalquantization to 24 bits is denoted herein as “P72” (24×3). Furthermore,normal coordinates may be reduced from 96 bits (32 bits per coordinate)to as little as 36 bits (12 bits per coordinate) with little visiblechange. Normal quantization to 12 bits per coordinate is denoted hereinas “N36” (12×3). While the location of specular highlights may differslightly with normal quantization, it is not visually apparent that suchchanges are reductions in quality.

Table 1 summarizes compression and other statistics for these objects.Column 1 notes the object in question, column 2 represents the number ofΔ's, and column three the Δ-strip length. The fourth column representssystem overhead per vertex (overhead being everything beyond positiontag/data, and normal tag/data). The “xyz quant” column denotesquantization thresholds, and the sixth column depicts the number ofbits/xyz. “Bits/tri” ninth column depicts bits per triangle.

The results in Table 1 are measured actual compression data except forestimated mesh buffer results, which are shown in parenthesis. No actualmesh buffer results were present in that applicant's prototype softwarecompressor did not yet implement a full meshifying algorithm. Theestimate (in parenthesis) assumes a 46% hit ratio in the mesh buffer.

In Table 1, the right-most column shows compression ratio performanceachieved over existing executable geometry formats. Although total bytecount of the compressed geometry is an unambiguous number, in stating acompression ratio some assumptions must be made about the uncompressedexecutable representation of the object. Applicant assumed optimizedgeneralized triangle strips, with both positions and normals representedby floating-point values to calculate “original size” data for Table 1.

To demonstrate the effect of pure 16-bit fixed point simple striprepresentation, Table 1 also shows byte count for the mode of OpenGL. Asshown, average strip length decreased in the range of 2-3. Few if anycommercial products take advantage of generalized triangle strips, andthus Table 1 considerably understates potential memory space savings.

TABLE 1 Δstp ovrhd/ xyz bits/ norm bits/ bits/ org'l size comp. sizecomp. Obj. name #Δ's len. vertex quant xyz quant norm tri (bytes)(bytes) ratio triceratops 6,039 15.9 7.5 48 30.8 18 16.8 55.9 179,70442,190 4.3X (35.0) (26,380) (6.9X) triceratops 6,039 15.9 7.5 30 17.8 1211.0 36.0 179,704 27,159 6.7X (24.4) (18,368) (9.8X) galleon 5,577 12.17.5 30 21.9 12 10.8 41.0 169,064 28,536 6.0X (27.2) (18,907) (9.0X)Viper 58,203 23.8 7.5 36 20.1 14 10.9 37.5 1,698,116 272,130  6.3X(25.0) (181,644)  (9.4X) 57 Chevy 31,762 12.9 7.5 33 17.3 13 10.9 35.8958,160 141,830  6.8X (24.3) (96,281) (10.0X) insect 263,783 3.0 7.5 3922.8 15 11.0 51.5 9,831,528 1,696,283  5.8X (33.9) (1,115,534)  (8.9X)

While certainly statistical variation exists between objects withrespect to compression ratios, general trends are nonetheless noted.When compressing using the highest quality setting of the quantizationknobs (P48/N18), compression ratios are typically about six. As ratiosapproach nearly then, most objects begin to show visible quantizationartifacts.

It will be appreciated from the foregoing, that a three-dimensionalgeometry compression algorithm may be implemented in real-time hardware,or in software. Significantly, if three-dimensional rendering hardwarecontains a geometry decompression unit according to the presentinvention, application geometry may be stored in memory in compressedformat. Further, data transmission may use the compressed format, thusimproving effective bandwidth for a graphics accelerator system,including shared virtual reality display environments. The resultantcompression can substantially increase the amount of geometry cacheablein main memory.

FIG. 7 is a detailed block diagram of the decompressor unit 130, shownin FIG. 1. As shown in FIG. 7, unit 130 includes a decompression inputfirst-in-first-out register (“FIFO”) 200 whose inputs include controlsignals and a preferably 32-bit or 64-bit data stream, which signals anddata stream preferably come from an accelerator port data FIFO (“APDF”)in interface unit 120 (see FIG. 1). The APDD portion of interface 120includes a controller that signals the size of the incoming data streamto unit 130. FIFO 200 provides output to an input block state machine220 and to an input block 210, state machine 220 and input block unit210 communicating with each other.

Output from block 210 is coupled to a barrel shifter unit 240 and to aHuffman table set 230, the output from the Huffman look-up being coupledto state machine 220. Opcode within state machine 220 processes thevalues provided by the Huffman tables 230 and outputs data to the barrelshifter unit 240. State machine 220 also provides an output to data pathcontroller 260, which outputs a preferably 12-bit wide signal to a tagdecoder unit 294 and also outputs data to the barrel shifter unit 240and to a normal processor 270, and a position/color processor 280.

Barrel shifter unit 240 outputs to the normal processor 270 and to aposition/color processor 280. The outputs from processors 270 and 280are multiplexed by output multiplexer unit 290 into a preferably 48-bitwide signal that is provided to a format converter 292. Decompressionunit 130 generates a preferably 12-bit tag that is sent to tag decoder294 in parallel with either 32-bits or 48-bits (for normals), that aresent to the format converter 292. These data streams provideinstructions that generate output to format converter 292. A preferably32-bit read-back path is used to read-back the state of the unit.

Table 2, below, shows interface signals used to implement decompressionunit 130 in the preferred embodiment:

TABLE 2 Signal Name Signals I/O Description id_data 64 I Data inputsfrom APDF id_tag 12 I Data on inputs is valid from APDF fd_stall 1 IStall signal from format converter di_busy 1 O Busy signal to statusregister di_faf 1 O Fifo-almost-full signal-to-input FIFO df_data 48 OData output to formal converter df_tag 12 O Tag output to tag decoderdu_context 32 O Context output to UPA section

Table 3, below, shows output data formats provided by unit 130 in thepreferred embodiment. As described herein, vertex, mesh bufferreference, and passthrough instructions generate transactions fromdecompression unit 130. Vertex and mesh buffer reference instructionssend data to the format converter, and each generates a headerindicating vertex replacement policy for the current vertex, followed bycomponent data. Each of these instructions always generates positiondata and, depending upon the value of the state register, may containcolor or normal data. All three of the normal components preferably aresent in parallel, whereas each position and color component isseparately sent. A passthrough instruction sends preferably 32-bits ofdata to the collection buffer.

TABLE 3 COMPONENTS FORMAT Header 32. Position s.15 Color s.15 Normals1.14(x3) Passthrough 32.

FIG. 8 is a detailed block diagram of the input block 210 depicted inFIG. 7. A preferably 64-bit input register 300 receives data from theAPDF portion of interface 130, with 32-bits or 64bits at a time beingloaded into register 300. Register 300 outputs preferably 32-bits at atime via multiplexer 310 to a first barrel shifter 320 whose outputpasses through a register 330 into a merge unit 340. The 64-bit outputfrom merge unit 340 is input to data register 350, part of whose outputis returned as input to a second barrel shifter 360. The output fromsecond barrel shifter 360 is passed through a register 370 and is alsoinput to merge unit 340. First barrel shifter 320 aligns data to thetail of the bit-aligned data stream being recycled from data register350 through second barrel shifter 360. The second barrel shifter 360shifts-off the used bits from data register 350.

FIG. 9 is a detailed block diagram of barrel shifter unit 240, shown inFIG. 7. In overview, barrel shifter unit 240 expands the variable-lengthposition, color, and normal index components to their fixed-pointprecisions. Data into unit 240 from unit 210 and/or 220 is input to aregister 400 whose output is shown as defining opcode and/or data units410, 420, 430, 440, 450, and 460, which are input to a multiplexer unit470.

Multiplexer unit 470 input A is used for the X component of the vertexinstruction, input B is used for the set normal instruction and thefirst component of the set color instructions, and input C is used forthe remaining components of the vertex and set color instructions. Unit240 further includes a barrel shift left register 480 coupled to receivetag_len data and to output to register 490, whose output in turn isinput to a barrel shift right register 500 that is coupled to receivedata_len data. Register 500 outputs to a mask unit 510 that is coupledto receive shift dfata and whose output is coupled to register 520,which outputs v_data. The output of data block 460 is coupled to aregister 530 whose output is coupled to a second register 540, whichoutputs pt_data.

An appropriate table within Huffman tables 230 (see FIG. 7) providesvalues of tag_len, data_len, and shift into units 480, 500 and 510,respectively. Barrel shift left unit 480 shifts the input data left by 0to 6 bits (tag_len), thus shifting off the Huffman tag. By contrast,barrel shift right register 500 shifts the data to the right by 0 to 16bits (16-data_len), and sign extends the data, thus bringing the data toits full size. Mask unit 510 masks off the lower ‘shift’ bits to clampthe data to the correct quantization level.

FIG. 10 depicts in greater block diagram detail the position/colorprocessor unit 280, shown in FIG. 7. Processor unit 280 generates finalposition or color component values. As shown in FIGS. 7 and 9, processorunit 280 receives a preferably 16-bit value (v_data) from the barrelshifter unit 240, specifically mask unit 510 therein.

If the abs_rel bit from the Huffman table 230 is set to relative, theincoming data are added by combiner unit 600 to the appropriate currentstored data. The new value passes through multiplexer 610, and is storedback into the register 620, and is sent along to the output multiplexer290, shown in FIG. 7. However, if the abs_rel bit is set to absolute,the incoming data bypasses adder 600, is latched into the register 620,and is also sent out to the output multiplexer 290.

As shown in FIG. 10, the position/color processor unit 280 furtherincludes a position/color mesh buffer 630 that is coupled to receive theinput to register 620. The output from mesh buffer 630 is coupled tomultiplexer gates, collectively 640, whose outputs reflect currentvalues of x, y, z, r, g, b and α. A register set, collectively shown as650, provides these current values to the input of a multiplexer 660,whose output is coupled to the adder 600. Processor unit 280 furtherincludes a register 670 that receives and outputs pt_data from barrelshifter unit 240.

As shown in FIG. 7, normal processor unit 270 also outputs data to theoutput multiplexer 290. FIG. 11A depicts in detail the sub-unitscomprising normal processor unit 270. As seen in FIG. 7 and FIG. 9, thenormal processor unit 270 receives an 18-bit normal index as threeseparate components: sextant/octant, u and v, or encoded Δu and Δvcomponents from mask unit 510 in barrel shifter unit 240. If the valueis a Δ-value (relative), the Δu and Δv are added to the current u and vvalues by respective adders 710. The intermediate values are stored andare also passed on to a fold unit 800 associated with decoder-fold-romunit 272 (see FIG. 11B).

As shown in FIG. 11A, the normal processor unit 270 further includesregisters 712, 714, 716, 718, 720, 722, 724, 726 which hold respectiveoctant, sextant, u and v values, curr_oct, curr_sext, curr_u and curr_vvalues. Also present in unit 270 are multiplexers 740, 742, 744, 746,748, 750, 752, 754, 756, 758 and 760, 1's complementing units 770, 772,latch-flipflop units 780, 782, 784 for holding respective v, u, and uvinformation, further adders 790, 792, and a normal mesh buffer 794coupled to receive curr_normal input components.

With reference to FIGS. 11A and 11B, for an absolute reference, the uand v values are passed directly to fold unit 800. The octant andsextant portions of the index are sent to decoder 810, within unit 272.Decoder 810 controls multiplexer 820 (which select constants), as wellas multiplexers 840, 842, 844, 860, 862, 864, which reorder components,and invert signs (using 2's complement units 850, 852, 854).

Fold unit 800 uses the u and v components of the normal index, from unit270, to calculate the address into the normal look-up table ROM 830. Theoctant and sextant fields, from unit 270, drive a decoder 810 thatdetermines sign and ordering of components output from the ROM look-uptable 830. Decoder 810 also handles special case normals not included inthe normal ROM look-up table 830.

FIG. 12 depicts interfaces to a mesh buffer, as shown in FIG. 10 and/orFIG. 11A. In the preferred embodiment, mesh buffer 794 is implemented asa register file and a pointer to the current location. Data is input tothe mesh buffer FIFO at the position of the current location pointer.However, random access to any of the 16 locations is allowed whenreading the data out of the FIFO by indexing off this pointer:address=(curr_loc_ptr−index)mod 16.

FIG. 13A depicts interfaces to Huffman tables, e.g., tables 230 in FIG.7. Huffman tables are used to decode the Huffman tags preceding thecompressed data. Three Huffman tables are used: one for position, forcolor, and for normal data, with each table preferably holding 64entries.

FIG. 13B depicts a preferred format for entry of position and color datain the Huffman tables, while FIG. 13C depicts the preferred format fornormal table entries. The instruction format for loading the Huffmantables in the compressed data stream is described later herein.

Several instructions generate data for the format converter 292, shownin FIG. 7, and appropriate tags must be generated for this data so theformat converter can correctly process the data. Table 4, below, showstags generated for the different data components. The components thatshow two tags may set the launch bit, and the second tag shows the valuewith the launch bit set.

TABLE 4 COMPONENTS TAG Header 0x020 X 0x011 Y 0x012 Z 0x013/0x413Nx/Ny/Nz 0x018/0x418 R 0x014 G 0x015 B 0x016/0x416 A 0x017/0x417 U0x0c0/0x4c0 V 0x01c/0x41c

Input block state machine 220 (see FIG. 7) includes a preferably six-bitstate register that holds information about the processing state of thedecompression unit. In the preferred embodiment, the following statebits are defined:

Bit 5: tex—Texture values in place of color

Bit 4: rnt—Replicate normal per vertex

Bit 3: rct—Replicate color per vertex

Bit 2: bnv—Normal bundled with vertex

Bit 1: bcv—Color bundled with vertex

Bit 0: cap—Color includes alpha (α)

Position/Color processor unit 280 (see FIGS. 7 and 10) preferablyincludes three 16-bit registers, curr_x, curr_y, and curr_z, whichcontain the current position components, X, Y, and Z, and are onlyupdated by vertex instructions.

Normal processor unit 270 (see FIGS. 7 and 11A) preferably includesthree six-bit registers, curr_oct, curr_sext, curr_u, curr_v) thatcontain the current normal. The first register holds the 3-bit sextantand octant fields, and the remaining two registers contain the u and vcoordinates for the normal. These values are written using the setnormal instruction, or they are updated by the vertex instruction if thebnv bit is set in the state register.

Position/color processor 280 further preferably includes four 16-bitregisters, curr_r, curr_g, curr_b, curr_a, which contain the currentcolor components, red, green, blue and alpha (α). These components areset using the se5t color instruction, or they are updated by the vertexinstruction if the bcv bit is set in the state register. In thepreferred embodiment, alpha is valid only if the cap bit is set in thestate register. The test bit is set when processing texture components,in which case only red and green are valid.

The instruction set implementing decompression according to the presentinvention will now be described. FIG. 14A depicts the vertex instructionformat, an instruction that uses variable-length Huffman encoding torepresent a vertex. Position information is always present in thisinstruction.

(REP) The vertex replacement policy is as follows:

00—Restart clockwise

01—Restart counter-clockwise

10—Replace middle

11—Replace oldest

(M) mesh buffer push:

0—No push

1—Push

With reference to FIG. 14A, the position data consists of avariable-length Huffman tag (0 to 6 bits) followed by three data fieldsof equal length for the X, Y, and Z components, which are eitherΔ-values or absolute values. The data_len field for the entry in theposition Huffman table gives the length of each of the X, Y, and Zfields, the tag_len entry gives the length of the tag, and the abs_relentry tells whether the data is absolute data or is relative to theprevious vertex. The shift entry from the Huffman table gives thequantization level (number of trailing zeroes) for the data.

If the bnv bit is set in the state register, a normal is included. Theencoded normal has a Huffman tag followed by either two variable-lengthdata fields for Δu and Δv, or a fixed-length field for the sextant andoctant (6 bits) followed by two variable-length fields for u and v. Theformer encoding is for delta encodings of normals, while the latterencoding is for absolute encodings. The data_len, tag_len, abs_rel, andshift fields from the normal Huffman table are used similarly as entriesfrom the position table.

FIG. 14B depicts vertex component data formats. If the bcv bit in thestate register is set, color is included with the vertex. The color isencoded similar the position, using three or four fields, but how thefields are used is determined by the tag table. If tagged absolute, thenx, y, z, r, g, b data is used. Absolute normals are used with sectantand octant fields. However, if the tag table indicates relative, deltanormals are used, and it sufficiences to send latitude and longitudedata (e.g., θ and φ, also referred to herein as u and v.

With further reference to FIG. 14B, a Huffman tag is followed by threeequal length fields for R, G, and B. The cap bit in the state registerindicates whether an additional field for α is included. The data_len,tag_len, abs_rel, and shift fields from the color Huffman table are usedsimilarly as for entries from the position and normal tables.

The states of the vertex instruction set are as follows:

1. Latch next opcode; output X; shift barrel shift right unit 500 (seeFIG. 10) by ptag_len+pdata_len−pquant+2.

2. Merge; output Header.

3. Output Y; shift barrel shift right unit 500 (see FIG. 9) bypdata_len−pquant.

4. Merge

5. Output Z; shift barrel shift right unit 500 (see FIG. 9) bypdata_len−pquant.

6. Merge.

a. If (bnv)

i. if (absolute normal), goto 7,

ii. else goto 9./*relative normal*/

b. else If (rnt), goto 21,

c. else If (bcv) goto 13,

d. else If (rct) goto 22,

e. else Merge; branch to next instruction.

7. Latch next opcode; output sextant/octant; shift barrel shift rightunit 500 (see FIG. 9) by ntag_len+6.

8. Merge.

9. Output U.

a. If (absolute normal), shift barrel shift right unit 500 (see FIG. 9)by ndata_len−nquant.

b. else/*relative normal*/, latch next opcode; shift Bs2 byntag_len+ndata_len−nquant

10. Merge.

11. Output V.

12. Merge.

a. If (bcv), goto 13,

b. else If (rct), goto 22,

c. else Merge; branch to next instruction.

13. Latch next opcode; output R; shift barrel shift right unit 500 (seeFIG. 9) by ctag_len+cdata_len−cquant.

14. Merge

15. Output G; shift barrel shift right unit 500 (see FIG. 9) bycdata_len−cquant.

16. Merge; if (tex), branch to next instruction.

17. Output B; shift barrel shift right unit 500 (see FIG. 9) bycdata_len−cquant.

18. Merge; if (^(˜)cap) branch to next instruction.

19. Output A; shift barrel shift right unit 500 (see FIG. 9) bycdata_len−cquant.

20. Merge; branch to next instruction.

21. Output curr_normal.

a. If (bcv), goto 13,

b. else If (rct), goto 22,

c. else Merge; branch to next instruction.

22. Output curr_r.

23. Output curr_g. If (tex), Merge; branch to next instruction

24. Output curr_b. If (^(˜)cap), Merge; branch to next instruction.

25. Output curr_a. Merge branch to next instruction.

FIG. 14C depicts the format for the set normal instruction. The setnormal instruction sets the value of the current normal registers. Thenormal data is encoded similarly as is normal data in the vertexinstruction, described herein. The states of the set normal instructionare as follows:

If (absolute normal)

1. Latch next opcode; output sextant/octant; shift barrel shift rightunit 500 (see FIG. 9) by ntag_len+8.

2. Merge.

3. Output U; shift barrel shift right unit 500 (see FIG. 9) byndata_len−nquant.

4. Merge.

5. Output V; shift barrel shift right unit 500 (see FIG. 9) byndata_len+nquant.

6. Merge; branch to next instruction.

else/*relative normal*/

1. Latch next opcode; output dU; shift barrel shift right unit 500 (seeFIG. 9) by n_tag_len+ndata_len−nquant.

2. Merge.

3. Output dV; shift barrel shift right unit 500 (see FIG. 9) byndata_len−nquant.

4. Merge; branch to next instruction.

FIG. 14D depicts the set color instruction, an instruction that sets thevalue of the current color registers. Encoding of the color data issimilar to encoding of the color data in the vertex instruction. Thestates of the set color instruction are as follows:

1. Latch next opcode; output R; shift barrel shift right unit 500 (seeFIG. 9) by ctag_len+cdata_len−cquant+2.

2. Merge.

3. Output G; shift barrel shift right unit 500 (see FIG. 9) bycdata_len−cquant.

4. Merge. If (tex), branch to next instruction.

5. Output B; shift barrel shift right unit 500 (see FIG. 9) bycdata_len−cquant.

6. Merge. If (^(˜)cap) branch to next instruction.

7. Output A; shift barrel shift right unit 500 (see FIG. 9) bycdata_len−cquant.

8. Merge; branch to next instruction.

FIG. 14E is the preferred format for the mesh buffer referenceinstruction. This instruction causes data from an entry in the meshbuffer to be sent out to the format converter as the next vertex. Withreference to FIG. 14E, the index indicates the entry from the meshbuffer to send. The newest entry in the mesh buffer has index 0, and theoldest has index 15. REP, the above-described replacement policy for thevertex instruction, is the same as used for the mesh buffer referenceinstruction. The states for the mesh buffer reference instruction are asfollows:

1. Latch next opcode; output Header; shift barrel shift right unit 500(see FIG. 9) by 9.

2. Output X from mesh buffer.

3. Output Y from mesh buffer.

4. Output Z from mesh buffer.

a. If (bnv or rn) goto 5,

b. else If (bcv or rct) goto 6,

c. else Merge; branch to next instruction.

5. If (bnv), output Normal from mesh buffer, else if (rnt) outputcurr_normal.

a. If (bnv or rct) goto 6,

b. else Merge; branch to next instruction.

6. If (bcv), output R from mesh buffer, else if (rct) output curr_r.

7. If (bcv), output G from mesh buffer, else if (rct) output curr_g. If(tex), Merge; branch to next instruction.

8. If (bcv), output B from mesh buffer, else if (rct) output curr_b. If(^(˜)cap), Merge; branch to next instruction.

9. If (bcv), output A from mesh buffer, else if (rct) output curr_a.Merge; branch to next instruction.

FIG. 14F depicts the set state instruction, which sets the bits thedecompression unit state register. The states for the set stateinstruction are as follows:

1. Latch next opcode; shift barrel shifter 2 by 11 bits.

2. Merge; branch instruction

3.

FIG. 14G depicts the set table instruction, which sets Huffman tableentries. The table selection is as follows:

00—Position table

01—Color table

10—Normal table

11—Undefined

The tag length is derived from the address. The nine bits in the entryfield correspond to the absolute/relative bit, data length, and shiftamount fields of the Huffman table entries. (The preferred format of theHuffman table entries has been described earlier herein.) The states ofthe set table instruction are as follows:

1. Latch next opcode; send address and entry to Huffman tables; shiftbarrel shift right unit 500 (see FIG. 9) by 23.

2. Merge; branch to next instruction.

Table 5 shows the preferred Huffman Table Fill Codes.

TABLE 5 Entries Fill Address Filled Tag Length Range 0tttttt 1 6 tttttt10ttttt 2 5 ttttt0-ttttt1 110tttt 4 4 tttt00-tttt11 1110ttt 8 3ttt000-ttt111 11110tt 16 2 tt0000-tt1111 111110t 32 1 t00000-t111111111110 64 0 Entire table

FIG. 14H depicts the passthrough instruction, which allows passthroughdata to be encoded in the compressed-data stream. The length of theinstruction preferably is 64-bits. Aligning successive passthroughinstructions to a 64-bit boundary allows for patching of passthroughdata in the encoded stream. The states for the passthrough instructionare as follows:

1. Latch next opcode; read address, shift barrel shift right unit 500(see FIG. 9) by 32 bits.

2. Merge.

3. Output data, shift barrel shift right unit 500 (see FIG. 9) by 32bits.

4. Merge; branch to next instruction.

FIG. 14I depicts the variable-length NOP (“VNOP) instruction, whichencodes a variable number of 0 bits in the data stream. The five-bitcount shown in FIG. 14I designates the number of 0 bits that follow.This instruction is implicitly used for the start of the data stream.This instruction may also be used to pad the data stream to 32-bit or64-bit boundaries, or encoding regions, for later patching. The statesfor this instruction are:

1. Latch next opcode; read count; barrel shift right unit 500 (see FIG.9) by 13 bits;

2. Merge.

3. Barrel shift right unit reads “count” positions;

4. Merge; branch to next instruction.

FIG. 14J shows the skip 8 instruction, whose states are:

1. Latch next opcode; shift barrel shift right unit 500 (see FIG. 9) by16 bits;

2. Merge; branch to next instruction.

It will be appreciated that it may be advantageous to reduce bandwidthrequirements between devices by not decompressing a data stream at asingle point in a decompression system. The present invention canprovide parallel decompression of a data stream by providing anadditional command advising the arrival of a given number of data wordsthat may be processed in parallel.

The present invention can recognize the presence of such parallelopportunities by the presence of mark bits, and cause the stated numberof data words to be shuttled to other processors within the system, forparallel decompression. Further, it is then permissible to jump aheadthe given number of words in the data stream to arrive at the next datathat is not eligible for parallel processing.

The present invention can also provide morphing capability to eliminateany abrupt perception gap in viewing a decompressed three-dimensionalobject. Within the decompressed data stream, it is possible to specifyvertices as linear or other interpolations of vertices that are actuallypresent or have previously been decompressed. Assume, for example, thatthe three-dimensional object is a tiger. At a far distance, no teeth arepresent in the tiger's mouth, yet at near distance teeth are present.The present invention can provide a seamless transition such that asdistance to the tiger shrinks, the teeth grow, with no sudden changeseen between a toothless tiger and a toothed tiger.

In some embodiments, the system and method described above may beconfigured as described in the following numbered paragraphs:

1. A method for decompressing compressed 3-D geometry data whichincludes a compressed representation of a first normal corresponding toa first vertex, comprising:

receiving said compressed representation of said first normal, whereinsaid compressed representation includes information identifying alocation of a first point on a predetermined sphere located in a firstcoordinate space;

forming a decompressed representation of said first normal utilizingsaid information identifying said location of said first point.

2. A method for decompressing compressed 3-D geometry data whichincludes a compressed representation of a first normal corresponding toa first vertex, comprising:

receiving said compressed representation of said first normal, whereinsaid compressed representation includes at least an index value;

receiving one or more mapping values usable to decompress said firstnormal;

selecting a first set of coordinate values using said index value,wherein said first set of coordinate values correspond to a first set ofcoordinate axes, wherein said first set of coordinate axes define afirst coordinate space which includes a predetermined sphere, whereinsaid first set of coordinate values identify a first point located in apredetermined region of a surface of said predetermined sphere;

mapping said first set of coordinate values to a second set ofcoordinate values using said one or more mapping values, wherein saidsecond set of coordinate values correspond to said first set ofcoordinate axes, and wherein said second set of coordinate valuesspecify a second point on said surface of said predetermined sphere;

and wherein said second set of coordinate values are usable to form adecompressed representation of said first normal.

3. The method of paragraph 2, wherein said compressed 3-D geometry dataincludes information describing a plurality of three-dimensionalvertices, wherein said plurality of three-dimensional vertices areusable to form a plurality of geometric primitives in order to representa surface of a three-dimensional graphical object.

4. The method of paragraph 2, wherein said selecting a first set ofcoordinate values includes using said index value to select said firstset of coordinate values from a plurality of predetermined sets ofcoordinate values, wherein each of said plurality of predetermined setsof coordinate values correspond to one of a plurality of predeterminedpoints within said predetermined region of said predetermined sphere.

5. The method of paragraph 4, wherein said index value includes a firstindex component and a second index component, wherein said first set ofcoordinate values are selected using both said first index component andsaid second index component.

6. The method of paragraph 5, wherein said first index component andsaid second index component are usable to locate points on atwo-dimensional coordinate grid.

7. The method of paragraph 6, wherein said first index component andsaid second index component are usable to locate points within saidpredetermined region of said surface of said predetermined sphere.

8. The method of paragraph 7, wherein said first coordinate space is anxyz coordinate space, and wherein said first set of coordinate axesinclude an x axis, a y axis, and a z axis.

9. The method of paragraph 8, wherein said predetermined sphere iscentered on an origin of said first set of coordinate axes.

10. The method of paragraph 9, wherein said first index component is avalue of an angle θ, wherein said angle θ is measured about said y axisto said first point, and wherein said second index component is a valueof an angle φ, wherein said angle φ is measured latitudinally from theplane at y=0 to said first point.

11. The method of paragraph 7, wherein said predetermined sphere iscentered on an origin of said first set of coordinate axes.

12. The method of paragraph 11, wherein said predetermined sphere is aunit sphere.

13. The method of paragraph 11, wherein said receiving said compressedrepresentation of said first normal includes:

receiving a header portion which includes a first tag value;

determining a length value of a body portion using said first tag value;

receiving said body portion using said length value determined from saidfirst tag value;

wherein said header portion and said body portion collectively includesaid compressed representation of said first normal.

14. The method of paragraph 13, further comprising using information insaid header portion to determine a first normalization coefficient forsaid first normal, wherein said first normalization coefficient isusable for scaling said first index component and said second indexcomponent to predetermined numeric ranges.

15. The method of paragraph 14, wherein said first normalizationcoefficient includes a first coefficient component and a secondcoefficient component.

16. The method of paragraph 15, further comprising using information insaid header value to determine a first absolute/relative value for saidfirst normal, wherein said first absolute/relative value indicates ifsaid first normal is absolutely specified or delta-encoded.

17. The method of paragraph 16, wherein said first absolute/relativevalue indicates that said first normal is absolutely specified.

18. The method of paragraph 17, wherein said one or mapping values areincluded in said compressed representation of said first normal.

19. The method of paragraph 18, further comprising scaling said firstindex component in accordance with said first coefficient component,thereby producing a first scaled index component, and further comprisingscaling said second index component in accordance with said secondcoefficient component, thereby producing a second scaled indexcomponent.

20. The method of paragraph 19, wherein said first scaled indexcomponent and said second scaled index component are usable to selectsaid first set of coordinate values from said plurality of predeterminedsets of coordinate values.

21. The method of paragraph 16, wherein said first absolute/relativevalue indicates that said first normal is delta-encoded relative to apreviously specified normal.

22. The method of paragraph 21, wherein said previously specified normalcorresponds to a third point on said surface of said predeterminedsphere, wherein said third point is identified by a third set ofcoordinate values, and wherein said third point is related to a fourthpoint within said predetermined region of said surface of saidpredetermined sphere by a first mapping, and wherein said fourth pointcorresponds to a fourth set of coordinate values previously selected bya previous index value.

23. The method of paragraph 22, wherein said selecting said first set ofcoordinate values includes adding said index value to said previousindex value in order to produce a final index value, wherein said finalindex value is usable to select said first set of coordinate values.

24. The method of paragraph 23, wherein said previous index valueincludes a previous first index component and a previous second indexcomponent, and wherein said final index value includes a final firstindex component and a final second index component.

25. The method of paragraph 24, wherein said adding said index value tosaid previous index value includes adding said first index component tosaid previous first index component, thereby generating said final firstindex component, and wherein said adding said index value to saidprevious index value further includes adding said second index componentto said previous second index component, thereby generating said finalsecond index value.

26. The method of paragraph 25, wherein said mapping said first set ofcoordinate values to said second set of coordinate values includesgenerating said second set of coordinate values from said first set ofcoordinate values using said first mapping.

27. The method of paragraph 26, further comprising scaling said firstindex component in accordance with said first coefficient component,thereby producing a first scaled index component, and further comprisingscaling said second index component in accordance with said secondcoefficient component, thereby producing a second scaled indexcomponent.

28. The method of paragraph 27, wherein said adding said index value tosaid previous index value includes adding said first scaled indexcomponent to said previous first index component to produce said finalfirst index component, and wherein said adding said index value to saidprevious index value further includes adding said second scaled indexcomponent to said previous second index component to produce said finalsecond index component.

29. The method of paragraph 28, wherein said final first index componentand said final second index component are usable to select said firstset of coordinate values from said plurality of predetermined sets ofcoordinate values.

30. A method for decompressing compressed 3-D geometry data whichincludes a compressed representation of a first normal corresponding toa first vertex, comprising:

receiving said compressed representation of said first normal, whereinsaid compressed representation includes at least an index value;

receiving one or more mapping values usable to decompress said firstnormal;

selecting a first set of coordinate values using said index value,wherein said first set of coordinate values correspond to a first set ofcoordinate axes, wherein said first set of coordinate axes define afirst coordinate space which includes a predetermined sphere centered onan origin of said first set of coordinate axes, wherein said first setof coordinate values identify a first point located in a first surfaceportion of said predetermined sphere, wherein said first surface portioncorresponds to a predetermined octant of said predetermined sphere;

mapping said first set of coordinate values to a second set ofcoordinate values using said one or more mapping values, wherein saidsecond set of coordinate values correspond to said first set ofcoordinate axes, and wherein said second set of coordinate valuesspecify a second point on said surface of said predetermined sphere;

and wherein said second set of coordinate values are usable to form adecompressed representation of said first normal.

31. The method of paragraph 30, wherein said index value includes afirst index component and a second index component, wherein said firstset of coordinate values are selected using both said first indexcomponent and said second index component.

32. The method of paragraph 31, wherein said first index component andsaid second index component are usable to locate points on atwo-dimensional coordinate grid.

33. The method of paragraph 32, wherein said first index component andsaid second index component are usable to locate points on saidpredetermined sphere which are within said first surface portion.

34. The method of paragraph 33, wherein said first coordinate space isan xyz coordinate space, and wherein said first set of coordinate axesinclude an x axis, a y axis, and a z axis.

35. The method of paragraph 34, wherein said first index component is avalue of an angle θ, wherein said angle θ is measured about said y axisto said first point, and wherein said second index component is a valueof an angle φ, wherein said angle φ is measured latitudinally from theplane at y=0 to said first point.

36. The method of paragraph 33, wherein said receiving said compressedrepresentation of said first normal includes:

receiving a header portion which includes a first tag value;

determining a length value of a body portion using said first tag value;

receiving said body portion using said length value determined from saidfirst tag value;

wherein said header portion and said body portion collectively includesaid compressed representation of said first normal.

37. The method of paragraph 36, further comprising using information insaid header portion to determine a first normalization coefficient forsaid first normal, wherein said first normalization coefficient isusable for scaling said first index component and said second indexcomponent to predetermined numeric ranges.

38. The method of paragraph 37, wherein said first normalizationcoefficient includes a first coefficient component and a secondcoefficient component.

39. The method of paragraph 38, further comprising using information insaid header value to determine a first absolute/relative value for saidfirst normal, wherein said first absolute/relative value indicates ifsaid first normal is absolutely specified or delta-encoded.

40. The method of paragraph 39, wherein said first absolute/relativevalue indicates that said first normal is absolutely specified.

41. The method of paragraph 40, wherein said one or mapping values areincluded in said compressed representation of said first normal.

42. The method of paragraph 41, wherein said one or more mapping valuesinclude an octant value which specifies a particular octant in whichsaid second point is located.

43. The method of paragraph 42, wherein said selecting a first set ofcoordinate values includes using said index value to select said firstset of coordinate values from a plurality of predetermined sets ofcoordinate values, wherein each of said plurality of predetermined setsof coordinate values correspond to one of a plurality of predeterminedpoints within said first surface portion of said predetermined sphere.

44. The method of paragraph 42, wherein said mapping said first set ofcoordinate values to said second set of coordinate values includes:

generating magnitudes of said second set of coordinate values by usingmagnitudes of said first set of coordinate values;

setting one or more sign bits of said second set of coordinate values byusing sign bits of points located within said particular octantspecified by said octant value.

45. The method of paragraph 44, further comprising scaling said firstindex component in accordance with said first coefficient component,thereby producing a first scaled index component, and further comprisingscaling said second index component in accordance with said secondcoefficient component, thereby producing a second scaled indexcomponent.

46. The method of paragraph 45, wherein said first scaled indexcomponent and said second scaled index component are usable to selectsaid first set of coordinate values from said plurality of predeterminedsets of coordinate values.

47. The method of paragraph 39, wherein said first absolute/relativevalue indicates that said first normal is delta-encoded relative to apreviously specified normal.

48. The method of paragraph 47, wherein said previously specified normalcorresponds to a third point on said surface of said predeterminedsphere, wherein said third point is identified by a third set ofcoordinate values, and wherein said third point is related to a fourthpoint within said first surface portion of said predetermined sphere bya first mapping, and wherein said fourth point corresponds to a fourthset of coordinate values previously selected by a previous index value.

49. The method of paragraph 48, wherein said one or more mapping valuesare included in a compressed representation of said previously specifiednormal.

50. The method of paragraph 49, wherein said one or more mapping valuesinclude a previous octant value which specifies a particular octant inwhich said third point is located.

51. The method of paragraph 50, wherein said second point is alsolocated in said particular octant.

52. The method of paragraph 50, wherein said selecting said first set ofcoordinate values includes adding said index value to said previousindex value in order to produce a final index value, wherein said finalindex value is usable to select said first set of coordinate values froma plurality of predetermined sets of coordinate values, wherein each ofsaid plurality of predetermined sets of coordinate values correspond toone of a plurality of predetermined points within said first surfaceportion of said predetermined sphere.

53. The method of paragraph 52, wherein said previous index valueincludes a previous first index component and a previous second indexcomponent, and wherein said final index value includes a final firstindex component and a final second index component.

54. The method of paragraph 53, wherein said adding said index value tosaid previous index value includes adding said first index component tosaid previous first index component, thereby generating said final firstindex component, and wherein said adding said index value to saidprevious index value further includes adding said second index componentto said previous second index component, thereby generating said finalsecond index value.

55. The method of paragraph 52, wherein said mapping said first set ofcoordinate values to said second set of coordinate values includes:

generating magnitudes of said second set of coordinate values by usingmagnitudes of said first set of coordinate values;

setting one or more sign bits of said second set of coordinate values byusing sign bits of said third set of coordinate values.

56. The method of paragraph 55, further comprising scaling said firstindex component in accordance with said first coefficient component,thereby producing a first scaled index component, and further comprisingscaling said second index component in accordance with said secondcoefficient component, thereby producing a second scaled indexcomponent.

57. The method of paragraph 56, wherein said adding said index value tosaid previous index value includes adding said first scaled indexcomponent to said previous first index component to produce said finalfirst index component, and wherein said adding said index value to saidprevious index value further includes adding said second scaled indexcomponent to said previous second index component to produce said finalsecond index component.

58. The method of paragraph 57, wherein said final first index componentand said final second index component are usable to select said firstset of coordinate values from said plurality of predetermined sets ofcoordinate values.

59. A method for decompressing compressed 3-D geometry data whichincludes a compressed representation of a first normal corresponding toa first vertex, comprising:

receiving said compressed representation of said first normal, whereinsaid compressed representation includes at least an index value;

receiving one or more mapping values usable to decompress said firstnormal;

selecting a first set of coordinate values using said index value,wherein said first set of coordinate values correspond to a first set ofcoordinate axes, wherein said first set of coordinate axes define afirst coordinate space which includes a predetermined sphere centered onan origin of said first set of coordinate axes, wherein said first setof coordinate values identify a first point located in a first surfaceportion of said predetermined sphere, wherein said first surface portioncorresponds to a predetermined sub-octant region of a second surfaceportion, wherein said second surface portion corresponds to apredetermined octant of said predetermined sphere;

mapping said first set of coordinate values to a second set ofcoordinate values using said one or more mapping values, wherein saidsecond set of coordinate values correspond to said first set ofcoordinate axes, and wherein said second set of coordinate valuesspecify a second point on said surface of said predetermined sphere;

and wherein said second set of coordinate values are usable to form adecompressed representation of said first normal.

60. The method of paragraph 59, wherein said index value includes afirst index component and a second index component, wherein said firstset of coordinate values are selected using both said first indexcomponent and said second index component.

61. The method of paragraph 60, wherein said first index component andsaid second index component are usable to locate points on atwo-dimensional coordinate grid.

62. The method of paragraph 61, wherein said first index component andsaid second index component are usable to locate points on saidpredetermined sphere which are within said first surface portion.

63. The method of paragraph 62, wherein said first coordinate space isan xyz coordinate space, and wherein said first set of coordinate axesinclude an x axis, a y axis, and a z axis.

64. The method of paragraph 63, wherein said first index component is avalue of an angle θ, wherein said angle θ is measured about said y axisto said first point on said predetermined sphere, and wherein saidsecond index component is a value of an angle φ, wherein said angle φ ismeasured latitudinally from the plane at y=0 to said first point on saidpredetermined sphere.

65. The method of paragraph 62, wherein said receiving said compressedrepresentation of said first normal includes:

receiving a header portion which includes a first tag value;

determining a length value of a body portion using said first tag value;

receiving said body portion using said length value determined from saidfirst tag value;

wherein said header portion and said body portion collectively includesaid compressed representation of said first normal.

66. The method of paragraph 65, further comprising using information insaid header portion to determine a first normalization coefficient forsaid first normal, wherein said first normalization coefficient isusable for scaling said first index component and said second indexcomponent of said first normal to predetermined numeric ranges.

67. The method of paragraph 66, wherein said first normalizationcoefficient includes a first coefficient component and a secondcoefficient component.

68. The method of paragraph 67, further comprising using information insaid header value to determine a first absolute/relative value for saidfirst normal, wherein said first absolute/relative value indicates ifsaid first normal is absolutely specified or delta-encoded.

69. The method of paragraph 68, wherein said first absolute/relativevalue indicates that said first normal is absolutely specified.

70. The method of paragraph 69, wherein said one or more mapping valuesare included in said compressed representation of said first normal.

71. The method of paragraph 70, wherein said one or more mapping valuesinclude an octant value and a sub-octant value, wherein said octantvalue specifies a particular octant of said predetermined sphere inwhich said second point is located, and wherein said sub-octant valuespecifies a particular sub-octant region within said second surfaceportion.

72. The method of paragraph 71, wherein said selecting a first set ofcoordinate values includes using said index value to select said firstset of coordinate values from a plurality of predetermined sets ofcoordinate values, wherein each of said plurality of predetermined setsof coordinate values correspond to one of a plurality of predeterminedpoints within said first surface portion of said predetermined sphere.

73. The method of paragraph 72, wherein said mapping said first set ofcoordinate values to said second set of coordinate values includes:

generating an intermediate set of coordinate values from said first setof coordinate values, wherein said intermediate set of coordinate valuescorrespond to an intermediate point located within said particularsub-octant region of said second surface portion;

generating magnitudes of said second set of coordinate values by usingmagnitudes of said intermediate set of coordinate values;

setting one or more sign bits of said second set of coordinate values byusing sign bits of said particular octant specified by said octantvalue.

74. The method of paragraph 73, further comprising scaling said firstindex component in accordance with said first coefficient component,thereby producing a first scaled index component, and further comprisingscaling said second index component in accordance with said secondcoefficient component, thereby producing a second scaled indexcomponent.

75. The method of paragraph 74, wherein said first scaled indexcomponent and said second scaled index component are usable to selectsaid first set of coordinate values from said plurality of predeterminedsets of coordinate values.

76. The method of paragraph 68, wherein said first absolute/relativevalue indicates that said first normal is delta-encoded relative to apreviously specified normal.

77. The method of paragraph 76, wherein said previously specified normalcorresponds to a third point on said surface of said predeterminedsphere, wherein said third point is identified by a third set ofcoordinate values, and wherein said third point is related to a fourthpoint within said first surface portion of said predetermined sphere bya first mapping, and wherein said fourth point corresponds to a fourthset of coordinate values previously selected by a previous index value.

78. The method of paragraph 77, wherein said one or more mapping valuesare included in a compressed representation of said previously specifiednormal.

79. The method of paragraph 78, wherein said one or more mapping valuesinclude a previous octant value which specifies a particular octant inwhich said third point is located, and wherein said one or more mappingvalues include a previous sub-octant value which specifies a particularsub-octant region within said second surface portion.

80. The method of paragraph 79, wherein said second point is alsolocated in said particular octant.

81. The method of paragraph 80, wherein third point is located within afirst sub-octant region of said particular octant.

82. The method of paragraph 81, wherein said second point is alsolocated within said first sub-octant region of said particular octant.

83. The method of paragraph 82, wherein said second point is in aneighboring sub-octant region to said first sub-octant region of saidparticular octant.

84. The method of paragraph 83, wherein said neighboring sub-octantregion shares an edge with said first sub-octant region of saidparticular octant.

85. The method of paragraph 79, wherein said selecting said first set ofcoordinate values includes adding said index value to said previousindex value in order to produce a final index value, wherein said finalindex value is usable to select said first set of coordinate values froma plurality of predetermined sets of coordinate values, wherein each ofsaid plurality of predetermined sets of coordinate values correspond toone of a plurality of predetermined points within said first surfaceportion of said predetermined sphere.

86. The method of paragraph 85, wherein said previous index valueincludes a previous first index component and a previous second indexcomponent, and wherein said final index value includes a final firstindex component and a final second index component.

87. The method of paragraph 86, wherein said adding said index value tosaid previous index value includes adding said first index component tosaid previous first index component, thereby generating said final firstindex component, and wherein said adding said index value to saidprevious index value further includes adding said second index componentto said previous second index component, thereby generating said finalsecond index value.

88. The method of paragraph 85, wherein said mapping said first set ofcoordinate values to said second set of coordinate values includes:

generating an intermediate set of coordinate values from said first setof coordinate values, wherein said intermediate set of coordinatesvalues correspond to a an intermediate point located within saidparticular sub-octant region of said second surface portion specified bysaid previous sub-octant value;

generating magnitudes of said second set of coordinate values by usingmagnitudes of said intermediate set of coordinate values;

setting one or more sign bits of said second set of coordinate values byusing sign bits of said particular octant specified by said previousoctant value.

89. The method of paragraph 88, further comprising scaling said firstindex component in accordance with said first coefficient component,thereby producing a first scaled index component, and further comprisingscaling said second index component in accordance with said secondcoefficient component, thereby producing a second scaled indexcomponent.

90. The method of paragraph 89, wherein said adding said index value tosaid previous index value includes adding said first scaled indexcomponent to said previous first index component to produce said finalfirst index component, and wherein said adding said index value to saidprevious index value further includes adding said second scaled indexcomponent to said previous second index component to produce said finalsecond index component.

91. The method of paragraph 90, wherein said final first index componentand said final second index component are usable to select said firstset of coordinate values from said plurality of predetermined sets ofcoordinate values.

92. A method for decompressing compressed 3-D geometry data whichincludes a compressed representation of a first normal corresponding toa first vertex, comprising:

receiving said compressed representation of said first normal, whereinsaid compressed representation includes at least an index value;

receiving one or more mapping values usable to decompress said firstnormal;

selecting a first set of coordinate values using said index value,wherein said first set of coordinate values correspond to a first set ofcoordinate axes, wherein said first set of coordinate axes define afirst coordinate space which includes a predetermined sphere, whereinsaid first set of coordinate values identify a first point located in afirst surface portion of said predetermined sphere, wherein said firstsurface portion corresponds to a predetermined sextant region of asecond surface portion, wherein said second surface portion correspondsto a predetermined octant of said predetermined sphere;

mapping said first set of coordinate values to a second set ofcoordinate values using said one or more mapping values, wherein saidsecond set of coordinate values correspond to said first set ofcoordinate axes, and wherein said second set of coordinate valuesspecify a second point on said surface of said predetermined sphere;

and wherein said second set of coordinate values are usable to form adecompressed representation of said first normal.

93. The method of paragraph 92, wherein said compressed 3-D geometrydata includes information describing a plurality of three-dimensionalvertices, wherein said plurality of three-dimensional vertices areusable to form a plurality of geometric primitives in order to representa surface of a three-dimensional graphical object.

94. The method of paragraph 92, wherein said index value includes afirst index component and a second index component, wherein said firstset of coordinate values are selected using both said first indexcomponent and said second index component.

95. The method of paragraph 94, wherein said first index component andsaid second index component are usable to locate points on atwo-dimensional coordinate grid.

96. The method of paragraph 95, wherein said first index component andsaid second index component are usable to locate points on saidpredetermined sphere which are within said first surface portion.

97. The method of paragraph 96, wherein said first coordinate space isan xyz coordinate space, and wherein said first set of coordinate axesinclude an x axis, a y axis, and a z axis.

98. The method of paragraph 97, wherein said predetermined sphere iscentered on an origin of said first set of coordinate axes.

99. The method of paragraph 97, wherein said first index component is avalue of an angle θ, wherein said angle θ is measured about said y axisto said first point on said predetermined sphere, and wherein saidsecond index component is a value of an angle φ, wherein said angle φ ismeasured latitudinally from the plane at y=0 to said first point on saidpredetermined sphere.

100. The method of paragraph 99, wherein said receiving said compressedrepresentation of said first normal includes:

receiving a header portion which includes a first tag value;

determining a length value of a body portion using said first tag value;

receiving said body portion using said length value determined from saidfirst tag value;

wherein said header portion and said body portion collectively includesaid compressed representation of said first normal.

101. The method of paragraph 100, further comprising using informationin said header portion to determine a first normalization coefficientfor said first normal, wherein said first normalization coefficient isusable for scaling said first index component and said second indexcomponent of said first normal to predetermined numeric ranges.

102. The method of paragraph 101, wherein said first normalizationcoefficient includes a first coefficient component and a secondcoefficient component.

103. The method of paragraph 102, further comprising using informationin said header value to determine a first absolute/relative value forsaid first normal, wherein said first absolute/relative value indicatesif said first normal is absolutely specified or delta-encoded.

104. The method of paragraph 103, wherein said first absolute/relativevalue indicates that said first normal is absolutely specified.

105. The method of paragraph 104, wherein said one or more mappingvalues are included in said compressed representation of said firstnormal.

106. The method of paragraph 105, wherein said one or more mappingvalues include an octant value and a sextant value, wherein said octantvalue specifies a particular octant of said predetermined sphere inwhich said second point is located, and wherein said sextant valuespecifies a particular sextant region within said second surfaceportion.

107. The method of paragraph 106, wherein said selecting a first set ofcoordinate values includes using said index value to select said firstset of coordinate values from a plurality of predetermined sets ofcoordinate values, wherein each of said plurality of predetermined setsof coordinate values correspond to one of a plurality of predeterminedpoints within said first surface portion of said predetermined sphere.

108. The method of paragraph 107, wherein said mapping said first set ofcoordinate values to said second set of coordinate values includes:

generating an intermediate set of coordinate values from said first setof coordinate values, wherein said intermediate set of coordinate valuescorrespond to an intermediate point located within a particular sextantregion of said second surface portion, wherein said particular sextantregion is specified by said sextant value;

generating magnitudes of said second set of coordinate values by usingmagnitudes of said intermediate set of coordinate values;

setting one or more sign bits of said second set of coordinate values byusing sign bits of said particular octant specified by said octantvalue.

109. The method of paragraph 108, wherein said generating saidintermediate set of coordinate values includes permuting x, y, and zcoordinates of said first set of coordinate values in order to fold saidfirst set of coordinate values about the planes x=y, y=z, and x=z withinsaid second surface portion, wherein said folded first set of coordinatevalues are usable as said intermediate set of coordinate values.

110. The method of paragraph 108, further comprising scaling said firstindex component in accordance with said first coefficient component,thereby producing a first scaled index component, and further comprisingscaling said second index component in accordance with said secondcoefficient component, thereby producing a second scaled indexcomponent.

111. The method of paragraph 110, wherein said first scaled indexcomponent and said second scaled index component are usable to selectsaid first set of coordinate values from said plurality of predeterminedsets of coordinate values.

112. The method of paragraph 103, wherein said first absolute/relativevalue indicates that said first normal is delta-encoded relative to apreviously specified normal.

113. The method of paragraph 112, wherein said previously specifiednormal corresponds to a third point on said surface of saidpredetermined sphere, wherein said third point is identified by a thirdset of coordinate values, and wherein said third point is related to afourth point within said first surface portion of said predeterminedsphere by a first mapping, and wherein said fourth point corresponds toa fourth set of coordinate values previously selected by a previousindex value.

114. The method of paragraph 113, wherein said one or more mappingvalues are included in a compressed representation of said previouslyspecified normal.

115. The method of paragraph 114, wherein said one or more mappingvalues include a previous octant value which specifies a particularoctant in which said third point is located, and wherein said one ormore mapping values include a previous sextant value which specifies aparticular sextant region within said second surface portion.

116. The method of paragraph 115, wherein said second point is alsolocated in said particular octant.

117. The method of paragraph 116, wherein said third point is locatedwithin a first sextant of said particular octant.

118. The method of paragraph 117, wherein said second point is alsolocated within said first sextant of said particular octant.

119. The method of paragraph 118, wherein said second point is locatedin a neighboring sextant to said first sextant of said particularoctant.

120. The method of paragraph 119, wherein said neighboring sextantshares an edge with said first sextant of said particular octant.

121. The method of paragraph 120, wherein said neighboring sextant islocated in a octant which is different from said particular octant.

122. The method of paragraph 115, wherein said selecting said first setof coordinate values includes adding said index value to said previousindex value in order to produce a final index value, wherein said finalindex value is usable to select said first set of coordinate values froma plurality of predetermined sets of coordinate values, wherein each ofsaid plurality of predetermined sets of coordinate values correspond toone of a plurality of predetermined points within said first surfaceportion of said predetermined sphere.

123. The method of paragraph 122, wherein said previous index valueincludes a previous first index component and a previous second indexcomponent, and wherein said final index value includes a final firstindex component and a final second index component.

124. The method of paragraph 123, wherein said adding said index valueto said previous index value includes adding said first index componentto said previous first index component, thereby generating said finalfirst index component, and wherein said adding said index value to saidprevious index value further includes adding said second index componentto said previous second index component, thereby generating said finalsecond index value.

125. The method of paragraph 122, wherein said mapping said first set ofcoordinate values to said second set of coordinate values includes:

generating an intermediate set of coordinate values from said first setof coordinate values, wherein said intermediate set of coordinatesvalues correspond to a an intermediate point located within saidparticular sextant region of said second surface portion specified bysaid previous sextant value;

generating magnitudes of said second set of coordinate values by usingmagnitudes of said intermediate set of coordinate values;

setting one or more sign bits of said second set of coordinate values byusing sign bits of said particular octant specified by said previousoctant value.

126. The method of paragraph 125, wherein said generating saidintermediate set of coordinate values includes permuting x, y, and zcoordinates of said first set of coordinate values in order to fold saidfirst set of coordinate values about the planes x=y, y=z, and x=z withinsaid second surface portion, wherein said folded first set of coordinatevalues are usable as said intermediate set of coordinate values.

127. The method of paragraph 125, further comprising scaling said firstindex component in accordance with said first coefficient component,thereby producing a first scaled index component, and further comprisingscaling said second index component in accordance with said secondcoefficient component, thereby producing a second scaled indexcomponent.

128. The method of paragraph 127, wherein said adding said index valueto said previous index value includes adding said first scaled indexcomponent to said previous first index component to produce said finalfirst index component, and wherein said adding said index value to saidprevious index value further includes adding said second scaled indexcomponent to said previous second index component to produce said finalsecond index component.

129. The method of paragraph 128, wherein said final first indexcomponent and said final second index component are usable to selectsaid first set of coordinate values from said plurality of predeterminedsets of coordinate values.

130. A computer system for decompressing compressed 3-D geometry datawhich includes a compressed representation of a first normalcorresponding to a first vertex, comprising:

an input unit coupled to receive said compressed representation of saidfirst normal, wherein said compressed representation includes at leastan index value, wherein said input unit is also configured to receiveone or more mapping values;

a look-up table unit coupled to receive said index value from said inputunit, wherein said look-up table unit is configured to output a firstset of coordinate values in response to receiving said index value,wherein said first set of coordinate values correspond to a first set ofcoordinate axes, wherein said first set of coordinate axes define afirst coordinate space which includes a predetermined sphere, whereinsaid first set of coordinate values identify a first point located in apredetermined region of a surface of said predetermined sphere;

a mapping unit coupled to receive said first set of coordinate valuesfrom said look-up table unit and said one or more mapping values fromsaid input unit, wherein said mapping unit is configured to generate asecond set of coordinate values from said first set of coordinate valuesusing said one or more mapping values, wherein said second set ofcoordinate values correspond to said first set of coordinate axes, andwherein said second set of coordinate values specify a second point onsaid surface of said predetermined sphere;

wherein said second set of coordinate values is usable to form adecompressed representation of said first normal.

131. The computer system of paragraph 130, wherein said compressed 3-Dgeometry data includes information describing a plurality ofthree-dimensional vertices, wherein said plurality of three-dimensionalvertices are usable to form a plurality of geometric primitives in orderto represent a surface of a three-dimensional graphical object.

132. The computer system of paragraph 130, wherein said look-up tableunit is configured to store a plurality of predetermined sets ofcoordinate values, wherein each of said plurality of predetermined setsof coordinate values correspond to one of a plurality of predeterminedpoints within said predetermined region of said predetermined sphere.

133. The computer system of paragraph 132, wherein said look-up tableunit is configured to select said first set of coordinate values fromsaid plurality of predetermined sets of coordinate values in response toreceiving said index value.

134. The computer system of paragraph 133, wherein said index valueincludes a first index component and a second index component, whereinsaid first set of coordinate values are selected using both said firstindex component and said second index component.

135. The computer system of paragraph 134, wherein said first indexcomponent and said second index component are usable to locate points ona two-dimensional coordinate grid.

136. The computer system of paragraph 135, wherein said first indexcomponent and said second index component are usable to locate pointswithin said predetermined region of said surface of said predeterminedsphere.

137. The computer system of paragraph 136, wherein said first coordinatespace is an xyz coordinate space, and wherein said first set ofcoordinate axes include an x axis, a y axis, and a z axis.

138. The computer system of paragraph 137, wherein said predeterminedsphere is centered on an origin of said first set of coordinate axes.

139. The computer system of paragraph 138, wherein said first indexcomponent is a value of an angle θ, wherein said angle θ is measuredabout said y axis to said first point, and wherein said second indexcomponent is a value of an angle φ, wherein said angle φ is measuredlatitudinally from the plane at y=0 to said first point.

140. The computer system of paragraph 136, wherein said predeterminedsphere is centered on an origin of said first set of coordinate axes.

141. The computer system of paragraph 140, wherein said predeterminedsphere is a unit sphere.

142. The computer system of paragraph 140, wherein said input unit isconfigured to receive a header data portion corresponding to said firstnormal.

143. The computer system of paragraph 142, further comprising a normaldecompression table which includes a plurality of sets of decompressionparameters usable for normal decompression.

144. The computer system of paragraph 143, wherein said input unit isconfigured to convey said header data portion to said normaldecompression table, and wherein said normal decompression table isconfigured to convey a first set of decompression parameters to saidinput unit in response thereto.

145. The computer system of paragraph 144, wherein said first set ofdecompression parameters is effectively selected by a first tag valueincluded in said header data portion.

146. The computer system of paragraph 145, wherein first set ofdecompression parameters are selected from the group consisting of: (i)a length value of said first tag value, (ii) a length value of a bodydata portion corresponding to said first normal, (iii) a firstnormalization coefficient corresponding to said first normal, and (iv) afirst absolute/relative value corresponding to said first normal.

147. The computer system of paragraph 146, wherein said header dataportion and said body data portion collectively include said compressedrepresentation of said first normal.

148. The computer system of paragraph 146, wherein said first set ofdecompression parameters includes said length value of said body dataportion, and wherein said input unit is configured to utilize saidlength value of said body data portion in receiving said body dataportion.

149. The computer system of paragraph 148, wherein said first set ofdecompression parameters includes said first absolute/relative value,and wherein said first absolute/relative value indicates that said firstnormal is absolutely specified.

150. The computer system of paragraph 149, wherein said first set ofdecompression parameters includes said first normalization coefficient,wherein said first normalization coefficient includes a firstcoefficient component and a second coefficient component.

151. The computer system of paragraph 150, wherein said input unit isconfigured to scale said first index component of said index valueaccording to said first coefficient component of said firstnormalization coefficient, thereby producing a first final indexcomponent.

152. The computer system of paragraph 151, wherein said input unit isconfigured to scale said second index component of said index valueaccording to said second coefficient component of said firstnormalization coefficient, thereby producing a second final indexcomponent.

153. The computer system of paragraph 152, wherein said input unit isconfigured to convey said first final index component and said secondfinal index component to said look-up table unit in order to select saidfirst set of coordinate values from said plurality of predetermined setsof coordinate values.

154. The computer system of paragraph 153, wherein said first finalindex component and said second final index component are usable tolocate points within said predetermined region of said predeterminedsphere.

155. The computer system of paragraph 148, wherein said first set ofdecompression parameters includes said first absolute/relative value,and wherein said first absolute/relative value indicates that said firstnormal is delta-encoded relative to a previously specified normal.

156. The computer system of paragraph 155, wherein said previouslyspecified normal corresponds to a third point on said surface of saidpredetermined sphere, wherein said third point is identified by a thirdset of coordinate values, and wherein said third point is related to afourth point within said predetermined region of said surface of saidpredetermined sphere by a first mapping, and wherein said fourth pointcorresponds to a fourth set of coordinate values previously selected bya previous index value.

157. The computer system of paragraph 155, wherein said input unit isconfigured to add said index value to said previous index value in orderto produce a final index value, wherein said input unit is configured toconvey said final index value to said look-up table unit in order toselect said first set of coordinate values.

158. The computer system of paragraph 157, wherein said previous indexvalue includes a previous first index component and a previous secondindex component, and wherein said final index value includes a finalfirst index component and a final second index component, and whereinsaid first normalization coefficient includes a first coefficientcomponent and a second coefficient component.

159. The computer system of paragraph 158, wherein said input unit isconfigured to add said first index component to said previous firstindex component in order to generate said final first index component,and wherein said look-up table unit is further configured to add saidsecond index component to said previous second index component in orderto generate said final second index component.

160. The computer system of paragraph 159, wherein said mapping unit isconfigured to generate said second set of coordinate values from saidfirst set of coordinate values using said first mapping.

161. The computer system of paragraph 158, wherein said input unit isconfigured to scale said first index component in accordance with saidfirst coefficient component, thereby producing a scaled first indexcomponent, and wherein said input unit is further configured to scalesaid second index component in accordance with said second coefficientcomponent, thereby producing a scaled second index component.

162. The computer system of paragraph 158, wherein said input unit isconfigured to add said scaled first index component to said previousfirst index component in order to generate said final first indexcomponent, and wherein said look-up table unit is further configured toadd said scaled second index component to said previous second indexcomponent in order to generate said final second index value.

163. The method of paragraph 162, wherein said final first indexcomponent and said final second index component are usable to selectsaid first set of coordinate values from said plurality of predeterminedsets of coordinate values.

164. The computer system of paragraph 130, wherein said predeterminedregion of said predetermined sphere is a predetermined octant of saidpredetermined sphere.

165. The computer system of paragraph 164, wherein said one or mappingvalues include an octant value specifying a particular octant of saidpredetermined sphere.

166. The computer system of paragraph 165, wherein said mapping unit isconfigured to generate magnitudes of said second set of coordinatevalues by using magnitudes of said first set of coordinate values, andwherein said mapping unit is configured to generate one or more signbits of said second set of coordinate values by using sign bits of saidparticular octant specified by said octant value.

167. The computer system of paragraph 130, wherein said predeterminedregion of said predetermined sphere is a predetermined sub-octant regionof a predetermined octant of said predetermined sphere.

168. The computer system of paragraph 167, wherein said one or mappingvalues include an octant value and a sub-octant value, wherein saidoctant value specifies a particular octant of said predetermined sphere,and wherein said sub-octant value specifies a particular sub-octantregion in said predetermined octant of said predetermined sphere.

169. The computer system of paragraph 168, wherein said mapping unit isconfigured to generate magnitudes of said second set of coordinatevalues by mapping said first point located in said predeterminedsub-octant region to said particular sub-octant region specified by saidsub-octant value.

170. The computer system of paragraph 169, wherein said mapping unit isconfigured to generate one or more sign bits of said second set ofcoordinate values by using sign bits of said particular octant specifiedby said octant value.

171. The computer system of paragraph 139, wherein said predeterminedregion of said predetermined sphere is a predetermined sextant region ofa predetermined octant of said predetermined sphere.

172. The computer system of paragraph 171, wherein said one or mappingvalues include an octant value and a sextant value, wherein said octantvalue specifies a particular octant of said predetermined sphere, andwherein said sextant value specifies a particular sextant region in saidpredetermined octant of said predetermined sphere.

173. The computer system of paragraph 172, wherein said mapping unit isconfigured to generate magnitudes of said second set of coordinatevalues by mapping said first point located in said predetermined sextantregion to said particular sextant region specified by said sextantvalue.

174. The computer system of paragraph 173, wherein said mapping unit isconfigured to generate one or more sign bits of said second set ofcoordinate values by using sign bits of said particular octant specifiedby said octant value.

175. The computer system of paragraph 173, wherein said mapping unit isconfigured to generate magnitudes of said second set of coordinates bypermuting xyz values of said first set of coordinates in order toperform foldings about the planes x=y, y=z, and x=z within saidpredetermined octant, wherein said foldings map said first point to athird point located in said particular sextant region specified by saidsextant value.

176. A memory media for storing program instructions for decompressingcompressed 3-D geometry data which includes a compressed representationof a first normal corresponding to a first vertex, wherein said programinstructions are executable to implement the steps of:

receiving said compressed representation of said first normal, whereinsaid compressed representation includes at least an index value;

receiving one or more mapping values usable to decompress said firstnormal, wherein said one or more mapping values are included in saidcompressed representation of said first normal if said first normal isabsolutely specified, and wherein said one or more mapping values areincluded in a compressed representation of a previously specified normalif said first normal is delta-encoded;

selecting a first set of coordinate values using said index value,wherein said first set of coordinate values correspond to a first set ofcoordinate axes, wherein said first set of coordinate axes define afirst coordinate space which includes a predetermined sphere centered onan origin of said first set of coordinate axes, wherein said first setof coordinate values identify a first point located in a predeterminedregion of a surface of said predetermined sphere;

mapping said first set of coordinate values to a second set ofcoordinate values using said one or more mapping values, wherein saidsecond set of coordinate values correspond to said first set ofcoordinate axes, and wherein said second set of coordinate valuesspecify a second point on said surface of said predetermined sphere;

and wherein said second set of coordinate values are usable to form adecompressed representation of said first normal.

Modifications and variations may be made to the disclosed embodimentswithout departing from the subject and spirit of the invention asdefined by the following claims.

What is claimed is:
 1. A computer-implemented method for renderingcompressed 3-D geometry data, the method comprising: receiving a set ofsaid compressed 3-D geometry data, wherein the set of compressed 3-Dgeometry data comprises compressed representations of normals, whereinthe compressed representations of normals comprise index values; anddecompressing the compressed 3-D geometry data by: accessing a tablecomprising a plurality of directions, wherein said plurality ofdirections are a particular representative subset of all possibledirections, using each index value to select a particular direction fromsaid table, and using the selected directions to form normals; and usingthe selected normals to render an image specified by the decompressed3-D geometry data.
 2. The method as recited in claim 1, wherein said allpossible directions are limited to a predetermined number ofsubstantially equally-spaced directions.
 3. The method as recited inclaim 1, wherein said all possible normals are limited to all possiblesubstantially equally-spaced normals specifiable given a predeterminednumber of bits.
 4. The method as recited in claim 1, wherein said allpossible normals are limited to all possible substantiallyequally-spaced normals specifiable given a predetermined resolution. 5.The method as recited in claim 1, wherein said plurality of directionsin said table are substantially equally-spaced directions within apredetermined contiguous range of directions.
 6. The method as recitedin claim 1, wherein said normals are unit normals.
 7. The method asrecited in claim 1, wherein said particular representative subset ofsaid all possible directions is a symmetrical representative subset ofsaid all possible directions.
 8. The method as recited in claim 1,wherein said index values are delta encoded relative to other indexvalues in said compressed 3-D geometry data.
 9. The method as recited inclaim 1, wherein said particular representative subset of said allpossible directions is limited to directions within a particular octantof a unit sphere representing all possible directions from a centerpoint of said unit sphere.
 10. The method as recited in claim 1, whereinsaid particular representative subset of said all possible directions islimited to directions within a particular sextant of a unit sphererepresenting all possible directions from a center point of said unitsphere.
 11. The method as recited in claim 1, wherein said particularrepresentative subset of said all possible directions is limited todirections within a particular sextant of a particular octant of a unitsphere representing all possible directions from a center point of saidunit sphere.
 12. The method as recited in claim 1, wherein saidparticular representative subset of said all possible directions islimited to directions within a particular fraction of a unit sphererepresenting all possible directions from a center point of said unitsphere.
 13. The method as recited in claim 1, wherein the compressedrepresentation includes a plurality of bits indicative of which of saidplurality of representative subsets is said particular representativesubset, wherein said representative subsets are symmetrical.
 14. Themethod as recited in claim 1, wherein said compressed representations ofnormals further include indicator bits, wherein said method furthercomprises using said indicator bits to adjust said selected directions.15. The method as recited in claim 1, wherein said compressedrepresentations of normals further include one or more indicator bits,wherein said particular direction comprises one or more directioncomponents, wherein said method further comprises performing signadjustments on said directions components based on said one or moreindicator bits.
 16. The method as recited in claim 1, wherein saidcompressed representations of normals further include one or moreindicator bits, wherein said particular direction comprises one or moredirection components, wherein said method further comprises adding oneor more adjustment constants to said one or more direction componentsbased on said one or more indicator bits.
 17. The method as recited inclaim 1, wherein said compressed representations of normals furtherinclude one or more indicator bits, wherein said indicator bits providegeneral direction information, wherein said method further comprisingusing the general direction information in combination with saidselected directions to form said normals.
 18. A method for renderingcompressed 3-D geometry data, the method comprising: receiving a set ofsaid compressed 3-D geometry data, wherein the set of compressed 3-Dgeometry data comprises compressed representations of normals, whereinthe compressed representations of normals comprise index values; anddecompressing the compressed 3-D geometry data by: accessing a tablecomprising a plurality of unit normals, wherein said plurality of unitnormals are a particular representative subset of all possible unitnormals, using each index value to select a particular unit normal fromsaid table; adjusting said unit normal based on one or more bits ofgeneral direction information included with said index values; and usingthe selected normals to render an image specified by the decompressed3-D geometry data.
 19. A computer program embodied on a carrier medium,wherein the computer program comprises a plurality of instructionsconfigured to: receive a set of compressed 3-D graphics data, whereinthe set of compressed 3-D geometry data comprises compressedrepresentations of normals, wherein the compressed representations ofnormals comprise index values; and decompress the compressed 3-Dgraphics data by: accessing a table comprising a plurality ofdirections, wherein said plurality of directions are a particularrepresentative subset of all possible directions, using each index valueto select a particular direction from said table, and using the selecteddirections to form normals; and use the selected normals to render animage specified by the decompressed 3-D graphics data.
 20. The computerprogram as recited in claim 19, wherein said carrier medium is acomputer-readable medium or a transmission medium.
 21. The computerprogram as recited in claim 19, wherein said all possible directions arelimited to a predetermined number of substantially equally-spaceddirections.
 22. The computer program as recited in claim 19, whereinsaid all possible normals are limited to all possible substantiallyequally-spaced normals specifiable given a predetermined number of bits.23. The computer program as recited in claim 19, wherein said allpossible normals are limited to all possible substantiallyequally-spaced normals specifiable given a predetermined resolution. 24.The computer program as recited in claim 19, wherein said plurality ofdirections in said table are substantially equally-spaced directionswithin a predetermined contiguous range of directions.
 25. The computerprogram as recited in claim 19, wherein said normals are unit normals.26. The computer program as recited in claim 19, wherein said particularrepresentative subset of said all possible directions is a symmetricalrepresentative subset of said all possible directions.
 27. The computerprogram as recited in claim 19, wherein said index values are deltaencoded relative to other index values in said compressed 3-D graphicsdata.
 28. The computer program as recited in claim 19, wherein saidparticular representative subset of said all possible directions islimited to directions within a particular octant of a unit sphererepresenting all possible directions from a center point of said unitsphere.
 29. The computer program as recited in claim 19, wherein saidparticular representative subset of said all possible directions islimited to directions within a particular sextant of a unit sphererepresenting all possible directions from a center point of said unitsphere.
 30. The computer program as recited in claim 19, wherein saidparticular representative subset of said all possible directions islimited to directions within a particular sextant of a particular octantof a unit sphere representing all possible directions from a centerpoint of said unit sphere.
 31. The computer program as recited in claim19, wherein said particular representative subset of said all possibledirections is limited to directions within a particular fraction of aunit sphere representing all possible directions from a center point ofsaid unit sphere.
 32. The computer program as recited in claim 19,wherein the compressed representation includes a plurality of bitsindicative of which of said plurality of representative subsets is saidparticular representative subset, wherein said representative subsetsare symmetrical.
 33. The computer program as recited in claim 19,wherein said compressed representations of normals further includeindicator bits, wherein said plurality of instructions are furtherconfigured to use said indicator bits to adjust said selecteddirections.
 34. The computer program as recited in claim 19, whereinsaid compressed representations of normals further include one or moreindicator bits, wherein said particular direction comprises one or moredirection components, wherein said plurality of instructions are furtherconfigured to perform sign adjustments on said directions componentsbased on said one or more indicator bits.
 35. The computer program asrecited in claim 19, wherein said compressed representations of normalsfurther include one or more indicator bits, wherein said particulardirection comprises one or more direction components, wherein saidplurality of instructions are further configured to add one or moreadjustment constants to said one or more direction components based onsaid one or more indicator bits.
 36. The computer program as recited inclaim 19, wherein said compressed representations of normals furtherinclude one or more indicator bits, wherein said indicator bits providegeneral direction information, wherein said wherein said plurality ofinstructions are further configured to use the general directioninformation in combination with said selected directions to form saidnormals.
 37. A graphics system comprising: a graphics processor, and aframe buffer, wherein said graphics processor is configured to receivecompressed 3-D graphics data, wherein the compressed 3-D graphics datacomprises index values, wherein the graphics processor is configured touse the index value to read a particular direction from a tablecomprising a plurality of different directions, wherein said pluralityof different directions comprises a subset of all possible directions,wherein the graphics processor is configured to use said particulardirections to generate normals, and wherein the graphics processor isconfigured to use said normals to render an image described by said 3-Dgraphics data into said frame buffer.
 38. The graphics system as recitedin claim 37, wherein said all possible directions are limited to apredetermined number of substantially regularly-spaced directions. 39.The graphics system as recited in claim 37, wherein said all possiblenormals are limited to all possible substantially regularly-spacednormals specifiable given a predetermined number of hits.
 40. Thegraphics system as recited in claim 37, wherein said all possiblenormals are limited to all possible substantially regularly-spacednormals specifiable given a predetermined resolution.
 41. The graphicssystem as recited in claim 37, wherein said plurality of directions insaid table are substantially regularly-spaced directions within apredetermined contiguous range of directions.
 42. The graphics system asrecited in claim 37, wherein said normals are unit normals.
 43. Thegraphics system as recited in claim 37, wherein said particularrepresentative subset of said all possible directions is a symmetricalrepresentative subset of said all possible directions.
 44. The graphicssystem as recited in claim 37, wherein said index values are deltaencoded relative to other index values in said compressed 3-D geometrydata.
 45. The graphics system as recited in claim 37, furthercomprising: a CPU; and a memory connected to said CPU, wherein saidgraphics processor is connected to said memory system; and a displaydevice connected to said frame buffer, wherein said frame buffer isconfigured to output said rendered image to said display device.